case study class 12 maths inverse trigonometry

CBSE Case Study Questions for Class 12 Maths Inverse Trigonometric Functions Free PDF

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CBSE Case Study Questions for Class 12 Maths Inverse Trigonometric Functions PDF

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Case Study Questions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions

• Last modified on: 1 year ago
• Reading Time: 4 Minutes

Case Study Questions:

Question 1:

The Government of India is planning to fix a hoarding board at the face of a building on the road of a busy market for awareness on COVID-19 protocol. Ram, Robert and Rahim are the three engineers who are working on this project. ‘A’ is considered to be a person viewing the hoarding board 20 metres away from the building, standing at the edge of a pathway nearby, Ram Robert and Rahim suggested to the film to place the hoarding board at three different locations namely C, D and E. ‘C’ is at the height of 10 metres from the ground level. For the viewer ‘A’, the angle of elevation of ‘D’ is double the angle of elevation of ‘C’. The angle of elevation of ‘E’ is triple the angle of elevation of ‘C’ for the same viewer.

Look at the figure given and based on the above information answer the following:

(i) Measure of ∠CAB = (a) tan –1 (2) (b) tan –1 (1/2) (c) tan– 1 (1) (d) tan –1 (3)

(ii) Measure of ∠DAB = (a) tan –1 (3/4) (b) tan –1 (3) (c) tan –1 (4/3) (d) tan –1 (4)

(iii) Measure of ∠EAB (a) tan –1 (11) (b) tan –1 (3) (c) tan –1 (2/11) (d) tan –1 (11/2)

(iv) A’ is another viewer standing on the same line of observation across the road. If the width of the road is 5 meters, then the difference between ∠CAB and ∠CA’B is (a) tan –1 (1/12) (b) tan –1 (1/8) (c) tan –1 (2/5) (d) tan –1 (11/21)

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Class 12 Maths: Case Study of Chapter 2 Inverse Trigonometric Functions PDF Download

• Post author: studyrate
• Post published:
• Post category: 12 board / Class 12
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In Class 12 Boards there will be Case studies and Passage Based Questions will be asked, So practice these types of questions. Study Rate is always there to help you. Free PDF Download of CBSE Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Case Study and Passage Based Questions with Answers were Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Inverse Trigonometric Functions  to know their preparation level.

Join our Telegram Channel, there you will get various e-books for CBSE 2024 Boards exams for Class 9th, 10th, 11th, and 12th.

In CBSE Class 12 Maths Paper, There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Inverse Trigonometric Functions Case Study Questions With answers

Here, we have provided case-based/passage-based questions for Class 12 Mathematics  Chapter 2 Inverse Trigonometric Functions

Case Study/Passage-Based Questions

Case Study 1:

Two men on either side of a temple of 30 meters high observe its top at the angles of elevation α and β respectively. (as shown in the figure above). The distance between the two men is 40√3 metres and the distance between the first person A and the temple is 30√3 meters. ∠CAB = α =

• A.sin -1 (2/√3)
• B.sin -1 (1/2)
• C.sin −1 (2)
• D.sin −1 (√3/2)

Answer: (B)

Hope the information shed above regarding Case Study and Passage Based Questions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions with Answers Pdf free download has been useful to an extent. If you have any other queries of CBSE Class 12 Mathematics Inverse Trigonometric Functions Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible. By Team Study Rate

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Chapter 2 Class 12 Inverse Trigonometric Functions

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Get NCERT Solutions of Chapter 2 Class 12 Inverse Trigonometry free at teachoo . Solutions of all exercise questions, examples are given, with detailed explanation.

In this chapter, first we learn

• What are inverse trigonometry functions, and what is their domain and range
• How are trigonometry and inverse trigonometry related - with triangles, and a cool explanation
• Finding principal value of inverse trigonometry functions like sin -1 , cos -1 , tan -1 , cot -1 , cosec -1 , sec -1
• Solving inverse trigonometry questions using formulas
• Then, solving by changing trigonometric variables ... like sin -1 to cos -1  or sec -1 to tan -1 and then applying formulas
• Also, there are some questions where we do not know if it can be solved via formula, it is not clear. So, we do them. Please look at them before the exams.

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NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions

Sushmita Sundas ,

Oct 26, 2023

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The NCERT solutions for class 12 Maths chapter 2 Inverse Trigonometric Functions includes topics like properties of Inverse Trigonometric functions and basic concepts. The detailed NCERT PDF is available here.

NCERT Solutions For Class 12 Maths Chapter 2 Inverse Trigonometric Functions can be downloaded here in the PDF format. In the solution, every significant topic is covered with a thorough explanation to aid students in better understanding the fundamental ideas. NCERT books are essential for both board exam and competitive exam preparation.

Numerous exercises are included in Inverse Trigonometric Functions. For the student's benefit, each exercise includes answers to all of the questions as well as a step-by-step solution. Students will find this to be very useful in both their practice sessions and their homework projects. Given below are the detailed NCERT Solutions For Class 12 Maths Chapter 2 Inverse Trigonometric Functions.

Table of Contents:

• NCERT Solutions For Class 12 Maths Chapter 2 Inverse Trigonometric Functions Download Link
• NCERT Solutions For Class 12 Maths Chapter 2 Inverse Trigonometric Functions Exercises
• Important Features of NCERT Solutions For Class 12 Maths Chapter 2 Inverse Trigonometric Functions
• Important Formulae in NCERT Solutions For Class 12 Maths Chapter 2

NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions PDF Download

The NCERT solutions for class 12 maths chapter 2 are provided in the table below for students to download. Students can click on the link and access the same. 

NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions Exercise-wise

In NCERT Solutions for class 12 Maths chapter 2 Inverse Trigonometric Functions, inverse trigonometric functions and their characteristics will be discussed with the students. By using the offered answers, students can become familiar with the domains and ranges (primary value branches) of Inverse trigonometry class 12.

Students should keep in mind when working through difficulties on this subject that the value of an inverse trigonometric function that is located in its primary value branch is referred to as the given inverse trigonometric function's principal value. The topics explained in inverse trigonometry class 12 include:

Students have previously learned about functions and the prerequisites for the inverse function's existence in prior classes. Students can discover the options for defining an inverse trigonometric function in the exercise 2.1 class 12 maths solutions. Given below are the solutions for NCERT Solutions for Class 12 Maths Chapter 2 for exercise 2.1 important questions:

Find the principal values of the following:

Question1 . Find the principal value of sin-1 (-1/2)

Question2. cos-1(√3/2)

Question3. cosec-1(2)

Question4. tan-1(-√3)

Question6. tan-1 (-1)

Question7. sec-1(2√3)

Question8. cot-1(√3)

Question9. cos-1(-1/√2)

Question10. cosec-1(-√2)

Find the value of the following:

Question11.

Question12.

Question13.

Therefore, option (B) is correct.

Question14. 

Exercise 2.2 - Basic Concepts

Through NCERT Solutions For Class 12 Maths Chapter 2 Inverse Trigonometric Functions for exercise 2.2, students may learn about trigonometric functions including sine, cosine, tangent, cot, cosec, and sec in this exercise.

Additionally, they may learn more in-depth information on the idea of an inverse trigonometric function, including how to determine its principal value and its domain and range. In addition, inverse trigonometric function graphs are also covered. Given below is the class 12 maths chapter 2 solutions for exercise 2.2:

Prove the following:

Question 4.

Write the following functions in the simplest form:

Question10.

Find the values of each of the following:

Question14. If then find the value of x

Question15. If

then find the value of x

Find the values of each of the expressions in Exercises 16 to 18.

Question16.

Question17.

Question18.

Question19.

Important Features of NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions

It is necessary to practise all the NCERT textbook questions of Class 12 Maths Chapter 2 to score good marks for the questions from this chapter. The NCERT Solutions For Class 12 Maths Chapter 2 Inverse Trigonometric Functions provided here have the following characteristics.

• The students' foundation in maths will be strengthened with the aid of NCERT solutions.
• Subject specialists carefully resolve each exercise.
• After revision, the students will be better able to understand each topic thoroughly and earn a decent grade.
• Students' confidence levels will rise as a result of these solutions.
• Since the solutions are written so that students can finish them quickly, it provides them the opportunity to work hard and get higher marks.

Important Formulae in NCERT Solutions Class 12 Maths Chapter 2

Students must utilise their critical thinking abilities while using the wide range of formulae provided in NCERT Solutions For Class 12 Maths Chapter 2 Inverse Trigonometric Functions. It is advised that they review the trigonometric formulae covered in earlier sessions because doing so will make it simpler for them to move into the main topic.

• sin –1 (–x) = – sin –1 x
• tan –1 x + cot –1 x = π/2
• sin –1 x + cos –1 x = π/2
• cos –1 (–x) = π – cos –1 x
• cot –1 (–x) = π – cot –1 x

Why are NCERT Solutions For Class 12 Maths Chapter 2 Inverse Trigonometric Functions important?

What are the important topics covered in NCERT Solutions For Class 12 Maths Chapter 2 Inverse Trigonometric Functions?

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Case study inverse trigonometry 2 chapter 2 class 12

Case study chapter 2 (inverse trigonometry).

Case study 2:- Read the following and answer the question.(Case study inverse trigonometry 1)

  Two men on either side of a temple 30 metres high observes its top at the angles of elevation α and β respectively. (as shown in the figure above). the distance between the two men is 40√3 metres and the distance between the first person A and the temple is 30√3 metres.

(i) ∠CAB = α =

(ii) ∠CAB = α =

(iii) ∠BCA = β = 

(iv) ∠ABC = 

(a) π/4                       (b) π/6

(c) π/2                         (d) π/3

(a) (-1, 1), (0, π)                (b) [-1, 1], (0, π)

(c) [-1, 1], [0, π]                 (d) (-1, 1), [-π/2, π/2]

Solution :We have

(i) Answer (b)

Now in ΔABD (right angled)

(ii) Answer (c) 

We have from (i)

(iii) Answer (d)

In right ΔBCD, we have

(iv) Answer (c)

ΔABC, we have,

∠ABC + ∠BAC  +  ∠ACB = 180°

⇒  ∠ABC + α + β = 180°

⇒  ∠ABC + 30 + 60 = 180

⇒  ∠ABC = 90

⇒  ∠ABC = π/2

(v) Answer (c)

Domain =[-1, 1]

Range = [0, π]

Some other Case study problem

Case study 1:-  The government of India is planning to fix a hoarding board at the face of a building on yhe road of bisy market for awaeeness on COVID-19 protocol. Ram , Robert and Rahim are the three engineers who are working on this project. “A” is considered to be person viewing the hoarding board 20 metres away from the building , standing at the edge of a pathwaynearby . Ram , Robert and Rahim suggested to the firm to place the hoarding board at three different locations namely C, D and E. “C” is at the height of  10 metres from the ground level. for the viewer A, the angle of elevation of “D” is double the angle of elevation of “C” the angle of elevation of “E” is triple the angle of elevation of “C” for the same viewer.(Case study inverse trigonometric 1 )

Solution: For solution click here

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Class 12 math (India)

Course: class 12 math (india)   >   unit 2.

• Unit test Inverse trigonometric functions

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Inverse Trigonometric Functions Class 12 MCQ Test (Online Available)

Free mcq test, table of content, inverse trigonometric functions test - 68.

Duration: 10 Mins

Maximum Marks: 10

Read the following instructions carefully.

1. The test contains 10 total questions.

2. Each question has 4 options out of which only one is correct .

3. You have to finish the test in 10 minutes.

4. You will be awarded 1 mark for each correct answer.

5. You can view your Score & Rank after submitting the test.

6. Check detailed Solution with explanation after submitting the test.

7. Rank is calculated on the basis of Marks Scored & Time

Inverse Trigonometric Functions Test - 67

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Duration:  10 Mins

4. There is No Negative marking .

5. You will be awarded 1 mark for each correct answer.

6. You can view your Score & Rank after submitting the test.

7. Check detailed Solution with explanation after submitting the test.

8. Rank is calculated on the basis of Marks Scored & Time.

Inverse Trigonometric Functions Test - 18

Duration: 30 Mins

Maximum Marks: 30

1. The test contains 30 total questions.

3. You have to finish the test in 30 minutes.

Inverse Trigonometric Functions Test - 15

1.  The test contains  10 total questions.

2.  Each question has  4 options  out of which  only one is correct .

3.  You have to finish the test in  10 minutes.

4.  There is  No Negative marking .

5.  You will be awarded  1 mark  for each correct answer.

6.  You can view your  Score & Rank  after submitting the test.

7.  Check  detailed Solution  with explanation after submitting the test.

8.  Rank is calculated on the basis of  Marks Scored & Time.

Inverse Trigonometric Functions Test - 14

Duration:  24 Mins

Maximum Marks:  12

1.  The test contains  12 total questions.

3.  You have to finish the test in  12 minutes.

Inverse Trigonometric Functions Test - 13

Duration:  25 Mins

Maximum Marks:  25

1.  The test contains  25 total questions.

3.  You have to finish the test in  25 minutes.

Inverse Trigonometric Functions Test - 10

Inverse trigonometric functions test - 9, inverse trigonometric functions test - 7, inverse trigonometric functions test - 6, inverse trigonometric functions test - 4, inverse trigonometric functions test - 2, inverse trigonometric functions test - 1.

One of the most significant chapters of Class 12 Maths is Inverse Trigonometric Functions. To improve your mathematical abilities, we, selfstudys.com, have the Inverse Trigonometric Functions Class 12 MCQ in online format. These Class 12 Inverse Trigonometric Functions MCQ are developed by the highly qualified subject matter experts. The Inverse Trigonometric Functions Class 12 MCQ are very useful for students for the understanding of the complex mathematical concepts. Selfstudys.com has taken an initiative in providing something different and something unique which can make Maths fun. You will have fun while practising Inverse Trigonometric Functions MCQ that we provide here on this site. 

The Class 12 Inverse Trigonometric Functions MCQ is developed as per the latest CBSE Curriculum for Maths. To secure good marks in the exam, you should regularly practise Class 12 Inverse Trigonometric Functions MCQ. 

To succeed at Maths, you need to do regular practice that is why we have created Class 12 Inverse Trigonometric Functions MCQ to help you practise. 

It is highly advisable for all the students to regularly practise these Inverse Trigonometric Functions in Class 12 MCQ daily even if it is only for 30 minutes. 

MCQ on Inverse Trigonometric Functions Class 12: Format 

Regular practice of Inverse Trigonometric Functions Class 12 MCQ will boost your memory, enhance problem solving and reasoning skills and will also make your mind sharp. It will help students to understand the mathematical topics well. 

Inverse Trigonometric Functions Class 12 MCQ are designed as per the last year’s question papers to give students an idea of the exam pattern. 

These Inverse Trigonometric Functions in Class 12 MCQ helps increase the confidence of the students who are stressed about the exam thinking about whether they will do good or not. 

How to Attempt the Inverse Trigonometric Functions Class 12 MCQ? 

Let’s have a look at how you can attempt the Class 12 Inverse Trigonometric Functions MCQ- 

• Go to the website i.e. selfstudys.com 

• Scroll down and select Class 12 

• Select Maths and click on the chapter Inverse Trigonometric Functions.

• After that, the Inverse Trigonometric Functions Class 12 MCQ page will appear and you can attempt it. 

Instructions of the Inverse Trigonometric Functions Class 12 MCQ 

• The total number of Questions in the Inverse Trigonometric Functions Class 12 MCQ will be 10. 
• In the Inverse Trigonometric Functions Class 12 MCQ, each Question will have 4 options out of which only 1 is correct. 
• The time duration for Class 12 Inverse Trigonometric Functions MCQ will be 10 minutes. 
• The student will be awarded 1 mark for each correct answer. 
• After completing and submitting the test, you can see your scores. 
• You can check the solutions with a detailed explanation of the test after submitting the Inverse Trigonometric Functions Class 12 MCQ. 
• On the basis of marks scored in the Inverse Trigonometric Functions Class 12 MCQ, your rank will be calculated. 
• You can also reattempt the MCQ. 

How to prepare for the Inverse Trigonometric Functions Class 12 MCQ?

Let’s discuss how you can prepare for the the Inverse Trigonometric Functions Class 12 MCQ 

• Visualise important formulas: Start by visualising important formulas of the Inverse Trigonometric Functions. As visualising the formulas help you understand and learn them and also score good marks in Inverse Trigonometric Functions Class 12 MCQ. 
• Logic behind the formulas: Learning Maths formulas will not solve the problem. There are a lot of formulas in Maths. To find the solution to the maths problem, you need to know when to use which formula. Knowing the back story behind the formulas can help students remember them and do wonders in the Class 12 Inverse Trigonometric Functions MCQ. 
• Read Formulas before sleeping: Thinking of something and then going to sleep often makes you dream about it and also makes one remember things. So why not use this trick to remember all the complex formulas to perform well in Inverse Trigonometric Functions Class 12 MCQ. 
• Write it down- Practising complex formulas by writing it down makes you learn them easily. Human brains are designed in this form that remember what we write as compared to what we read. You can remember all the mathematical formulas unconsciously for a long time by writing them again and again. It is also advisable for all the students to practise these formulas before attempting the Inverse Trigonometric Functions Class 12 MCQ. 
• Do not hurry to memorise all the Mathematical formulas at once: Do not panic by thinking about learning all the formulas in one day. If you try to learn all the formulas in a single day, you will end up panicking, stressed and remembering nothing. 

The Inverse Trigonometric Functions Class 12 MCQ to Improve Scores in Maths

The first thing which a student wants to know after finishing their syllabus is whether they can score well in the exam or not. The Inverse Trigonometric Functions Class 12 MCQ helps students to understand the mathematical concepts and also in which particular area they are lacking. 

Understand the Pattern of the Inverse Trigonometric Functions Class 12 MCQ

Inverse Trigonometric Functions Class 12 is an important chapter which requires regular practice. The MCQ questions of this chapter can help students to do regular practice. The pattern of the Inverse Trigonometric Functions Class 12 MCQ is simple. Students will have one question and 4 options out of which only 1 will be correct. 3 options will be given to test the understanding of the concept of the student. The Class 12 Inverse Trigonometric Functions MCQ makes sure that the student is learning all the concepts deeply. 

It is advisable for all the students to go through the notes and formulas before starting the Inverse Trigonometric Functions Class 12 Maths MCQ . 

Benefits of the Inverse Trigonometric Functions Class 12 MCQ

• Time Management: One of the best benefits of the Inverse Trigonometric Functions Class 12 MCQ is that a student learns to manage their time effectively. As the time duration of the Inverse Trigonometric Functions Class 12 MCQ will only be 10 minutes, it can be helpful for students as they will have more time to do revision. 
• Created by Selfstudys Subject Matter Experts: The Inverse Trigonometric Functions Class 12 MCQ are developed by the highly qualified subject matter experts of selfstudys which have expertise in the teaching industry and are familiar with the pattern of the examination. 
• Fast and Easy: The Class 12 Inverse Trigonometric Functions MCQ is relatively fast and easy to score when compared with offline exams. 
• Gives the idea of the pattern of the exam to the students: The Inverse Trigonometric Functions Class 12 MCQ gives the idea of the pattern of the exam to the students which can help them to score well. 
• Improve the skills of the students: The Inverse Trigonometric Functions Class 12 MCQ can significantly improve the problem solving, arithmetic and time management skills. 

Tips for Solving Inverse Trigonometric Functions Class 12 MCQ

Let’s discuss the tips which can be helpful for all the students before solving the Inverse Trigonometric Functions Class 12 MCQ.

• Read the full question: Students are advised to read the question of the Class 12 Inverse Trigonometric Functions MCQ completely as it allows them to understand it better. Students often get excited by looking at the question and without reading the entire question, choose the most logical answer. This is a very common mistake which students make. 
• Answer it in your mind first: Try answering the question in your mind after reading the Inverse Trigonometric Functions Class 12 MCQ. Do not look at the options. Try to answer it without looking at the options as it will help you to be completely sure about the answer. 
• Attempt the questions which you know first: While attempting the Inverse Trigonometric Functions Class 12 MCQ, if you are not sure about a particular answer, skip it for the time being and move on to the next question. This will ensure time management as time management is very important for students and help them to become more efficient. 
• Make an educated guess: You can make an educated guess while attempting the Inverse Trigonometric Functions Class 12 MCQ as there is no negative marking for incorrect answers. So you can calmly attempt all the questions. 
• Sticking with your first-choice is not always the best option- After reading the Class 12 Inverse Trigonometric Functions MCQ, it is generally the best way to stick to one option. It is completely different to second guess yourself and switch the option which you selected at first. However, it does not mean that the first option you selected was the correct one. The subject experts will intentionally add the most common wrong options in the Inverse Trigonometric Functions Class 12 MCQ that seem correct but are not. 

How to Select the Correct Answers to the Inverse Trigonometric Functions Class 12 MCQ? 

• Use the process of elimination: After reading the entire questions and options in the Inverse Trigonometric Functions Class 12 MCQ, you can use the process of elimination for the options for which you are completely sure that they are incorrect. Even if you know the correct option, it is advisable for all the students to use the process of elimination. 
• “All of the above” and “None of the above”: While attempting the Inverse Trigonometric Functions Class 12 MCQ, if you come across options like “All of the above” and “none of the above”, do not choose them unless you are confident as students feel that this might be the correct answer. This mistake is very common among students. 
• Read every option of the question: It is advisable for all the students to read each and every option of the Class 12 Inverse Trigonometric Functions MCQ before choosing the final option. There is always the best answer to every MCQ, you may end up not selecting the best one. 
• Find the answers hidden in the question: After reading the Inverse Trigonometric Functions Class 12 MCQ, try decoding the questions because many times the answers are found in the questions itself. 
• True or False Test: Doing a true or false test in the Inverse Trigonometric Functions Class 12 MCQ can be very beneficial as it can be easier for a student to eliminate all the false answer options and choosing the correct answer. 
• A possibility when there are two correct answers- When two answer options look correct in the Class 12 Inverse Trigonometric Functions MCQ, with an ‘All of the above’ option, then possibly it is the correct answer option. 

How Time Management can be Achieved by Attempting the Inverse Trigonometric Functions Class 12 MCQ? 

When practising Maths, time management is very important. The first step while attempting the Inverse Trigonometric Functions Class 12 MCQ is to divide your time into segments to avoid last minute rush. Estimate how long a question will take. Always attempt the easy questions first. 

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12th Class Mathematics Inverse Trigonometric Functions Question Bank

Done case based (mcqs) - inverse trigonometric functions total questions - 10.

A) \[{{\sin }^{-1}}\left( \frac{2}{\sqrt{3}} \right)\] done clear

B) \[{{\sin }^{-1}}\left( \frac{1}{2} \right)\] done clear

C) \[{{\sin }^{-1}}\left( 2 \right)\] done clear

D) \[{{\sin }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\] done clear

question_answer 2) \[\angle CAB=\alpha =\]

A) \[{{\cos }^{-1}}\left( \frac{1}{5} \right)\] done clear

B) \[{{\cos }^{-1}}\left( \frac{2}{5} \right)\] done clear

C) \[{{\cos }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\] done clear

D) \[{{\cos }^{-1}}\left( \frac{4}{5} \right)\] done clear

question_answer 3) \[\angle BCA=\beta =\]

A) \[{{\tan }^{-1}}\left( \frac{1}{2} \right)\] done clear

B) \[{{\tan }^{-1}}\left( 2 \right)\] done clear

C) \[{{\tan }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\] done clear

D) \[{{\tan }^{-1}}\left( \sqrt{3} \right)\] done clear

question_answer 4) \[\angle ABC=\]

A) \[\frac{\pi }{4}\] done clear

B) \[\frac{\pi }{6}\] done clear

C) \[\frac{\pi }{2}\] done clear

D) \[\frac{\pi }{3}\] done clear

question_answer 5) Domain and Range of \[{{\cos }^{-1}}x=\]

A) \[\left( -1,\,\,1 \right),\,\left( 0,\,\,\pi  \right)\] done clear

B) \[\left[ -1,\,\,1 \right],\,\left( 0,\,\pi  \right)\] done clear

C) \[\left[ -1,\,1 \right],\,\left[ 0,\,\,\pi  \right]\] done clear

D) \[\left( -1,\,\,1 \right),\,\left[ -\frac{\pi }{2},\frac{\pi }{2} \right]\] done clear

A) \[{{\tan }^{-1}}\left( 2 \right)\] done clear

B) \[{{\tan }^{-1}}\left( \frac{1}{2} \right)\] done clear

C) \[{{\tan }^{-1}}\left( 1 \right)\] done clear

D) \[{{\tan }^{-1}}\left( 3 \right)\] done clear

question_answer 7) Measure of \[\angle DAB=\]

A) \[{{\tan }^{-1}}\left( \frac{3}{4} \right)\] done clear

B) \[{{\tan }^{-1}}\left( 3 \right)\] done clear

C) \[{{\tan }^{-1}}\left( \frac{4}{3} \right)\] done clear

D) \[{{\tan }^{-1}}(4)\] done clear

question_answer 8) Measure of \[\angle EAB=\]

A) \[{{\tan }^{-1}}\left( 11 \right)\] done clear

B) \[{{\tan }^{-1}}3\] done clear

C) \[{{\tan }^{-1}}\left( \frac{2}{11} \right)\] done clear

D) \[{{\tan }^{-1}}\left( \frac{11}{2} \right)\] done clear

question_answer 9) A' is another viewer standing on the same line of observation across the road. If the width of the road is 5 meters, then the difference between \[\angle CAB\]and \[\angle CA'B\]is

A) \[{{\tan }^{-1}}\left( 1/2 \right)\] done clear

B) \[{{\tan }^{-1}}\left( \frac{1}{12} \right)\] done clear

C) \[{{\tan }^{-1}}\left( \frac{2}{5} \right)\] done clear

D) \[{{\tan }^{-1}}\left( \frac{11}{21} \right)\] done clear

question_answer 10) Domain and Range of \[{{\tan }^{-1}}x=\]

A) \[{{R}^{+}},\,\left( -\frac{\pi }{2},\,\frac{\pi }{2} \right)\] done clear

B) \[{{R}^{-}},\,\left( -\frac{\pi }{2},\,\frac{\pi }{2} \right)\] done clear

C) \[R,\,\left( -\frac{\pi }{2},\,\frac{\pi }{2} \right)\] done clear

D) \[R,\,\left( 0,\,\frac{\pi }{2} \right)\] done clear

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Case Based (MCQs) - Inverse Trigonometric Functions

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Class 12 Maths Chapter 2 Inverse Trigonometric Functions MCQs

Class 12 Maths Chapter 2 Inverse Trigonometric Functions MCQs are available here with the correct answers and solutions. MCQs of Class 12 Maths Chapter 2 covers all the concepts of the NCERT curriculum, such as the restrictions on domains and ranges of trigonometric functions, which ensure the existence of their inverses and observe their behaviour through graphical representations. These MCQs will help Class 12 students to prepare for the board exam 2022-2023. All these MCQs are given here based on the latest CBSE guidelines for Class 12 students.

Get MCQs for all the chapters of Class 12 Maths along with solutions here.

MCQs for Chapter 2 Inverse Trigonometric Functions

The expert teachers solved all the MCQs of chapter 2, Inverse trigonometric functions of Class 12 Maths. Each of these multiple-choice questions contains a correct answer and an explanation. Students must solve these multiple-choice questions to understand how to apply all the concepts and formulas of Class 12 Maths.

Also, check:

• Inverse Trigonometric Functions for Class 12
• Important Questions for Class 12 Maths Chapter 2

Practising MCQs of Chapter 2 Class 12 Maths will help boost your confidence in recognising the methods of solving any problem that appears in the CBSE 2022-2023 board exam.

Download PDF – Inverse Trigonometric Functions MCQs

Mcqs for chapter 2 inverse trigonometric functions with answers.

1. The principal value of tan -1 (tan 3π/5) is

Correct option: (b) -2π/5

tan -1 (tan 3π/5)

This can be written as:

tan -1 (tan 3π/5) = tan -1 (tan[π – 2π/5])

= tan -1 (- tan 2π/5) {since tan(π – x) = -tan x}

= –tan -1 (tan 2π/2)

2. sin[π/3 – sin -1 (-½)] is equal to:

Correct option: (d) 1

= sin(π/3 + π/6)

3. The domain of sin –1 (2x) is

Let sin –1 (2x) = θ.

Thus, 2x = sin θ.

As we know, – 1 ≤ sin θ ≤ 1

We can write this as– 1 ≤ 2x ≤ 1, which gives -1/2 ≤ x ≤ 1/2.

Therefore, the domain of sin-1(2x) is [-½, ½].

4. If sin –1 x + sin –1 y = π/2, then value of cos –1 x + cos –1 y is

Correct option: (a) π/2

sin –1 x + sin –1 y = π/2

(π/2) + (π/2) – (π/2) = cos -1 x + cos -1 y

Therefore, cos –1 x + cos –1 y = π/2.

5. Which of the following is the principal value branch of cos –1 x?

(d) (0, π) – {π/2}

The principal value branch of cos –1 x is [0, π].

6. The value of the expression sin [cot –1 (cos (tan –1 1))] is

Correct option: (d) √(2/3)

= sin[cot -1 {cos (tan -1 (tan π/4))}] {since tan π/4 = 1}

= sin [sin -1 (√(⅔))] {by Pythagoras theorem}

7. The domain of y = cos –1 (x 2 – 4) is

Correct option: (d)

y = cos –1 (x 2 – 4 )

⇒ cos y = x 2 – 4

As we know, –1 ≤ cos y ≤ 1

So, – 1 ≤ x 2 – 4 ≤ 1

Adding 4 on both sides, we get;

⇒ 3 ≤ x 2 ≤ 5

Taking square root on both sides, we get;

⇒ √3 ≤ x ≤ √5

8. If α ≤ 2 sin –1 x + cos –1 x ≤ β, then

(a) α = -π/2, β = π/2

(b) α = 0, β = π

(c) α = -π/2, β = 3π/2

(d) α = 0, β = 2π

Correct option: (b) α = 0, β = π

α ≤ 2 sin –1 x + cos –1 x ≤ β

We know that,

-π/2 ≤ sin –1 x ≤ π/2

⇒ (-π/2) + (π/2) ≤ sin –1 x + (π/2) ≤ (π/2) + (π/2)

⇒ 0 ≤ sin –1 x + (sin –1 x + cos –1 x) ≤ π

⇒ 0 ≤ 2 sin –1 x + cos –1 x ≤ π

By comparing with α ≤ 2 sin –1 x + cos –1 x ≤ β, we get α = 0, β = π.

9. The value of sin (2 tan –1 (.75)) is equal to

(d) sin 1.5

Correct option: (c) .96

sin (2tan –1 (.75))

Let, tan –1 (.75) = θ

tan θ = 0.75

tan θ = 3/4

Thus by Pythagoras theorem, we get;

sin θ = 3/5 and cos θ = 4/5.

sin (2tan –1 (.75)) = sin 2θ {as tan -1 (.75) = θ}

= 2 sin θ cos θ

= 2 × (3/5) × (4/5)

Therefore, sin (2tan–1 (.75)) = .96.

10. sin(tan -1 x), where |x| < 1, is equal to:

(a) x/√(1 – x 2 )

(b) 1/√(1 – x 2 )

(c) 1/√(1 + x 2 )

(d) x/√(1 + x 2 )

Correct option: (d) x/√(1 + x 2 )

Let tan -1 x = θ.

So, tan θ = x = x/1

From this, we can write the sin θ and cos θ values as:

sin θ = x/√(1 + x 2 )

cos θ = 1/√(1 + x 2 )

sin(tan -1 x) = sin θ = x/√(1 + x 2 ).

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• Health Disparities in TBI
• Comparing Head Impacts
• Clinical Guidance
• Mild Traumatic Brain Injury Management Guideline
• Resources for Health Care Providers

Traumatic Brain Injury & Concussion

About Moderate and Severe TBI

Preventing TBI

Symptoms of Mild TBI and Concussion

Where to Get Help

Facts About TBI

For Medical Professionals

Clinical Guidance for Pediatric mTBI

Health Care Provider Resources

CDC Programs

HEADS UP Online Training Courses

National Concussion Surveillance System

Core State Injury Prevention Program (Core SIPP)

A traumatic brain injury, or TBI, is an injury that affects how the brain works. TBI is a major cause of death and disability in the United States.

For Everyone

Health care providers.