# Exam Question for Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions

Please refer to below Exam Question for Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions. These questions and answers have been prepared by expert Class 12 Mathematics teachers based on the latest NCERT Book for Class 12 Mathematics and examination guidelines issued by CBSE, NCERT, and KVS. We have provided Class 12 Mathematics exam questions for all chapters in your textbooks. You will be able to easily learn problems and solutions which are expected to come in the upcoming class tests and exams for standard 10th.

## Chapter 2 Inverse Trigonometric Functions Class 12 Mathematics Exam Question

All questions and answers provided below for Exam Question Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions are very important and should be revised daily.

**Exam Question Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions**

**Very Short Answer Type Questions**

**Question.**

**Answer.**

**Question.** **Write the principal value of**

**Answer.**

**Question.** **Using principal values, write the value of**

**Answer.** Principal value of

**Question. **

**Answer.**

**Question. ** **Write the principal value of**

**Answer.**

**Question. **

**Answer.**

**Question.** **Using principal value, nd the value of**

**Answer.**

**Question. If tan ^{−1} (√3) + cot^{−1} (x) = π/2, then find x.**

Answer.

**Question.**

**Answer.**

**Question.** **Write the principal value of**

**Answer.**

**Question.** **Find the principal value of**

**Answer.** Principal value of

**Question.** **Write the principal value of tan ^{−1} (√3)− cot^{−1} (−√3)**

**Answer.**tan

^{−1}(√3)− cot

^{−1}(−√3)

**Question. **

**Answer.** We know that, sin^{–1}(sin x) = x

**Question.**

**Answer.**

**Question.**

**Answer.**

**Question.** **Find the value of the following :**

**Answer.**

** Question. If cos(tan^{-1} x + cot^{-1 }√3) = 0 then the value of x is ………** cos(tan

Answer.

^{-1}x + cot

^{-1 }√3) = 0

** Question. The set of values of sec^{-1} 1/2 is ……… .**Since, domain of sec

Answer.

^{-1}x is R – (-1, 1).

**Question.****The value of cos(sin-1 x + cos-1 x) where |x| ≤ 1, is ……… .**

**Answer.**

**Question.**

**Answer.**

**Question.** **The value of cot ^{-1} (-x ) x ∈ R in terms of cot^{-1} x is ……… .**

**Answer.**We know that,

**Short Answer Type Questions**

**Question.**

**Answer.**

**Question.**

**Answer.**

**Question.**

**Answer.**

**Question. If 2tan ^{-1} (cos θ) tan^{-1} (2cosec θ) then show that θ = π/4, where n is any integer.**

**• Thinking Process**

**Answer.**

**Question.**

**Answer.**

**Question.**

**Answer.**

**Question.** Prove that

**Answer.**

**Question.** Prove that :

**Answer.**

**Question.** Prove that

**Answer.**

**Question.** Solve for x : 2 tan** ^{–1}**(cos x) = tan

^{–1}(2cosec x)

**Answer.**tan

^{–1}(cos x) = tan

^{–1}(2cosec x)

⇒ 2 tan

^{–1}(cosx) – tan

^{–1}(2cosecx) = 0

**Question.** Prove that

**Answer.**

**Question.****Solve the equation for x :****sin ^{–1}x + sin^{–1}(1–x) = cos^{–1}x**

**Answer.**

⇒ sin^{–1} x + sin^{–1} x = cos^{–1}(1− x)

⇒ 2sin^{–1}x = cos^{–1}(1–x) ⇒ cos(2sin^{–1}x) = (1 – x)

⇒ 1 – 2 sin^{2}(sin^{–1} x) = (1 – x) ⇒ 2sin^{2} (sin^{–1} x) = x

⇒ 2x^{2 }= x ⇒ 2x^{2} – x = 0 ⇒ x (2x –1) = 0

⇒ x = 0 or 2x – 1 = 0 ⇒ x = 0 or x = 1/2

**Question.**

**Answer.**

**Question.** Solve for x :

**Answer.**

**Question.** Prove that :

**Answer.** L.H.S.

**Question.** If sin [cot^{–1 }(x + 1)] = cos (tan** ^{–1 }**x), then find x.

**Answer.**We have, sin[cot

^{–1}(x + 1)] = cos (tan

^{–1}x) … (1)

Let cot

^{–1}(x + 1) = A and tan

^{–1}x = B

**Question.** If (tan** ^{–1}x)^{2}** +(cot

^{−1}x)

^{2}= 5π

^{2}/8 then find x.

**Answer.**

**Question.****Prove the following:**

**Answer.** L.H.S.

**Question.** Solve for x :**tan^{−1} (x + 1) + tan^{−1} (x – 1) = tan^{−1} 8/31**

**Answer**. We have, tan

^{−1}(x + 1) + tan

^{−1}(x – 1) = tan

^{−1}8/31

**Question.**

**Answer.**

** Question. Solve for x : tan^{−1}(2 ) + tan^{−1}(3x)** =

**π**/4

**Answer.**We have, tan

^{−1}(2 ) + tan

^{−1}(3x) = π/4

**Question.**

**Answer.**

**Question.** Prove that

**Answer.**

**Question.** Solve for x :

**Answer.** We have,

**Question.** Prove that

**Answer.** L.H.S.

**Question.** Prove that

**Answer.** Putting x = cos θ, we get

**Question.** Solve for x : tan^{−1 }x + 2cot** ^{−1 }** x = 2π/3

**Answer.**

**Question.** Prove that :

**Answer.**

**Question.** Find the value of the following :

**Answer.**

**Question.****Prove that :**

**Answer.**

**Question.** Show that:

**Answer.**

**Question.****Prove the following**

**Answer.**

**Question.** Prove that :

**Answer.**

**Question.****Prove that :**

**Answer.**

**Question.** Prove that :

**Answer.**

**Question.** Prove that :

**Answer.**

**Question.****Write into the simplest form:**

**Answer.**

**Question.** Prove that :

**Answer.**

**Long Answer Type Questions**

**Question.**

**Answer.** We have,

**Question.**

**Answer.**

**Question.**

**Answer.**

**Question.** If a_{1}, a_{2}, a_{3}, …, an is a_{n} arithmetic progression with common difference**d, then evaluate the following expression.**

**Answer.**

**Question.** **Write into the simplest form:**

**Answer.**