Please refer to Inverse Trigonometric Functions Class 12 Mathematics Important Questions with solutions provided below. These questions and answers have been provided for Class 12 Mathematics based on the latest syllabus and examination guidelines issued by CBSE, NCERT, and KVS. Students should learn these problem solutions as it will help them to gain more marks in examinations. We have provided Important Questions for Class 12 Mathematics for all chapters in your book. These Board exam questions have been designed by expert teachers of Standard 12.

## Class 12 Mathematics Important Questions Inverse Trigonometric Functions

**Very Short Answer Type Questions**

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**Short Answer Type Questions**

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

**Answer.**

**Question.** Solve for x:

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**Question.** Solve for x :**sin ^{−1} (1 – x) – 2 sin^{−1} x = π/2**

**Answer.**

**Question.****Solve for x :**

**Answer.**

⇒ (x + 6) (x – 1) = 0 ⇒ x = –6, x = 1

But x = – 6 does not satisfy the equation.

∴ x = 1 is the only solution.

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

**Answer.**

**Question.** Solve for x : cos(2 sin^{-1}x) = 1/9. x > 0**Answer.** The given equation is

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

**Answer.** Putting x = tan^{2}θ, we get

**Question.** Solve for x :

**Answer.**

**Question.** Prove that: cot^{–1} 7 + cot^{–1} 8 + cot^{–1}18 = cot^{–1}3.**Answer.** L.H.S. = cot^{–1} 7 + cot^{–1} 8 + cot^{–1} 18

**Question.** Prove that :

**Answer.**

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

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**Question.****Solve for x :**

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

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**Question. Find the real solution of**

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**Long Answer Type Questions**

**Question. Find the simplified form of**

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

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

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

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

**Answer.**

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

**Answer.**

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

**Answer.**

**Question.** **Find the principal value of sec ^{–1}(–2).**

**Answer.**Let sec

^{–1}(–2) = y. Then, sec y = –2.

**Question. Using the principal values, evaluate the following :**

**Answer.**

**Question.** **Using principal values, evaluate the following.**

**Answer.** We know that the range of principal value

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

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

**Question.**

**Answer.**

**Question.** **Find the principal value of tan ^{–1}(–1).**

**Answer.**Let tan

^{–1}(–1) = x ⇒ –1 = tan x

We know that the range of principal value branch

**Question.** **If tan ^{−1 }x + tan^{-1} y = π/4 xy < 1, then write the value of x + y + xy.**

**Answer.**

**Question. Find the principal value of tan ^{−1}√3 −sec^{−1}(−2).**

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**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 meters and the distance between the first person A and the temple is 30√3 meters. Based on the above information answer the following:**

** Question. ∠𝐶𝐴𝐵 = 𝛼=**a. sin

^{−1}(2/√3)

b. sin

^{−1}(1/2)

c. sin

^{−1}(2)

d. sin

^{−1}(√3/2)

## Answer

B

** Question. ∠𝐶𝐴𝐵 = 𝛼=**a. cos

^{−1}(1/5)

b. cos

^{−1}(2/5)

c. cos

^{−1}(√3/2)

d. cos

^{−1}(4/5)

## Answer

C

** Question. ∠𝐵𝐶𝐴= 𝛽=**a. tan

^{−1}(1/2)

b. tan

^{−1}(2)

c. tan

^{−1}(1/√3)

d. tan

^{−1}(√3)

## Answer

D

** Question. ∠𝐴𝐵𝐶 =**a. 𝜋/4

b. 𝜋/6

c. 𝜋/2

d. 𝜋/3

## Answer

C

** Question. Domain and Range of cos^{−1}𝑥=**a. ( −1, 1 ), (0 ,𝜋)

b. [ −1, 1 ], (0 ,𝜋)

c. [ −1, 1 ], [0 ,𝜋]

d. ( −1, 1 ) , [−𝜋/2,𝜋/2]

## Answer

C