CBSE Class 12th Mathematics Chapter 2 - Inverse Trigonometric Functions Important Questions with Answers

You should focus on solving CBSE Class 12th Mathematics Chapter 2: Inverse Trigonometric Functions important questions, especially to help you score high marks. By solving CBSE Class 12th Mathematics 2 questions, you will be solving exam-oriented questions only.

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Inverse Trigonometric Functions play a crucial role in higher mathematics, offering a way to determine angles when the values of trigonometric ratios are known. Chapter 2 of CBSE Class 12 Mathematics, dedicated to this topic, builds on the fundamental trigonometric functions studied in earlier classes and extends their application to inverse relationships. Understanding these functions is essential for solving complex mathematical problems in calculus, coordinate geometry, and even physics. The chapter explains inverse trigonometric functions' domain and range concepts and how to determine their principal values together with their properties along with their graphical representations. The functions assist in the definition of angles throughout the quadrantal regions while finding extensive application within engineering practices, architectural contexts, and scientific explorations. The properties of inverse trigonometric functions simplify calculations in integration and differentiation, making them a key topic in higher mathematics.

To help students gain a strong grasp of this chapter, we have compiled important questions with answers that cover all major aspects of inverse trigonometric functions. The study material consists of three categories of questions about theoretical concepts as well as numerical problems and real-world applications to fully prepare students for board exams. The questions will help students develop better problem-solving capacities and better understand inverse trigonometric relations. Students who practice these essential questions will obtain competence and accuracy when working on board exam questions. Students who practice these questions will receive comprehensive support for their revision because they learn to evaluate functions for principal values and simplify expressions through properties while solving real-world mathematical problems. The important questions along with answers from CBSE Class 12 Mathematics Chapter 2 serve as a fundamental resource for students who study for examinations. Conceptual knowledge is enhanced through this material while establishing solid preparation for future mathematics-based studies and admission exams like JEE and other entrance exams. Prepare thoroughly with the most important questions of CBSE Class 12th Mathematics Chapter 2 - Inverse Trigonometric Functions. You can first cover the CBSE Class 12th Mathematics syllabus to understand the key topics and then start solving the CBSE Class 12th Mathematics Chapter 2 - Inverse Trigonometric Functions Important Question to get a better understanding of your preparation level. Start practicing now.

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Write the value of
tan^-1 (?3) – cot^-1 (- ?3). (All India 2019,13)

Question 2.

Solve for X,
tan^-1 (x + 1) + tan^-1 (x – 1) = tan^-1\(\frac{8}{31}\). (All India 2019,15)

Question 3.

Find the value of sin (cos^-1 + tan^-1\(\frac{2}{3}\)). (All India 2019)

Question 4.

Solve for x, tan^-1 3x + tan^-1 2x = \(\frac{\pi}{4}\). (Delhi 2019. 2015, 2013C)

Question 5.

Solve tan^-1 4x + tan^-1 6x = \(\frac{\pi}{4}\) (Delhi 2019)

Question 6.

Find the principal value of
tan^-1?3 – sec^-1 (- 2). (CBSE 2018 C; All India 2012)

Question 7.

Prove that
3 sin^-1x = sin^-1(3x – 4x³), x ? \(\left[-\frac{1}{2}, \frac{1}{2}\right]\). (CBSE 2018)

Question 8.

Prove that
\(\tan ^{-1} \frac{1}{5}+\tan ^{-1} \frac{1}{7}+\tan ^{-1} \frac{1}{3}+\tan ^{-1} \frac{1}{8}=\frac{\pi}{4}\) (DelhI 2018; Foreign 2015; Delhi 2008; 2008C)

Question 9.

If tan^-1\(\frac{x-3}{x-4}\) + tan \(\frac{x+3}{x+4}=\frac{\pi}{4}\), then find the value of x. (All India 2017)

Question 10.

Solve the following equation for x.
cos(tan^-1 x) = sin(cot^-1\(\frac{3}{4}\)) (Delhi 2017, Foregin 2014; All India 2013)

Question 1.

Solve for x,
2 tan^-1x (cos x) = tan^-1 (2 cosecx). (Delhi 2016; Foreign 2015, Delhi 2014C; All India 2009)

Question 2.

Solve for x,
tan^-1(x – 1) + tan^-1 x + tan^-1(x + 1) = tan^-1 3x (All India 2016)

Question 3.

Prove that
tan^-1\(\left(\frac{6 x-8 x^{3}}{1-12 x^{2}}\right)\) – tan^-1\(\left(\frac{4 x}{1-4 x^{2}}\right)\) = tan^-1 2x; |2x| < \(\frac{1}{\sqrt{3}}\). (All India 2016)

Question 4.

Prove that
cot^-1\(\left(\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right)\) = \(\frac{x}{2}\), 0 < x < \(\frac{\pi}{2}\), or x ? \(\frac{\pi}{4}\)
(Foreign 2016; Delhi 2014, 2011; All India 2009)

Question 5.

Solve for x,
tan^-1\(\left(\frac{x-2}{x-1}\right)\) – tan^-1\(\left(\frac{x+2}{x+1}\right)\) = \(\frac{\pi}{4}\) (Foreign 2016)

Question 6.

If sin [cot^-1 (x + 1)] = cos (tan^-1 x), then find x. (Delhi 2015)

Question 7.

If(tan^-1 x)² + (cot^-1 x)² = \(\frac{5 \pi^{2}}{8}\), then find x. (Delhi 2015)

Question 8.

Prove the following.
Inverse Trigonometric Functions Class 12 Maths Important Questions Chapter 2 37

(All India 2015)

Question 9.

Inverse Trigonometric Functions Class 12 Maths Important Questions Chapter 2 38

then find the value of ?. (Foregin 2015)

Question 10.

Prove that
2 tan^-1\(\left(\frac{1}{2}\right)\) + tan^-1\(\left(\frac{1}{7}\right)\) = sin^-1\(\left(\frac{31}{25 \sqrt{2}}\right)\) (All India 2015C)