# NCERT Solutions for Class 12th: Ch 2 Inverse Trigonometric Functions Miscellaneous Exercise

#### NCERT Solutions for Class 12th: Ch 2 Inverse Trigonometric Functions Miscellaneous Exercise Math

Page No: 51

**Miscellaneous Exercise on Chapter 2**

Find the value of the following:

Question: 1

**Answer**

Question: 2

**Answer**

Prove that

Question: 3

**Answer**

Question: 4

**Answer**

Question: 5

**Answer**

Question: 6

**Answer**

Question: 7

Exercise 2.1 Inverse Trigonometry

**Answer**

Question: 8

**Answer**

Page No. 52

Prove that

Question: 9

**Answer**

Question: 10

**Answer**

Question: 11

**Answer**

Question: 12

**Answer**

Solve the following equations:

Question: 13

**Answer**

Question: 14

**Answer**

Question: 15

**Answer**

The correct option is D.

Question: 16

sin

^{–1}(1 – x) – 2 sin^{–1}x = Ï€/2, then x is equal to
(A) 0, 1/2

(B) 1, 1/2

(C) 0

(D) 1/2

Answer

Given that sin

^{–1}(1 − x) − 2sin^{–1}x = Ï€/2
Let x = sin y

∴ sin

^{–1}(1 − sin y) − 2y = Ï€/2
⇒ sin

^{–1}(1 − sin y) = Ï€/2 + 2y
⇒ 1 − sin y = sin (Ï€/2 + 2y)

⇒ 1 − sin y = cos 2y

⇒ 1 − sin y = 1 − 2sin

^{2}y [as cos^{2}y = 1−2sin^{2}y]
⇒ 2sin

^{2}y − sin y = 0
⇒ 2x

^{2}− x = 0 [as x = sin y]
⇒ x(2x − 1) = 0

⇒ x = 0 or, x = 1/2

But x = 1/2 does not satisfy the given equation.

∴ x = 0 is the solution of the given equation.

The correct option is C.

Question: 17

tan

^{–1}(x/y) − tan^{–1}(x-y/x+y) is equal to
(A) Ï€/2

(B) Ï€/3

(C) Ï€/4

(D) -3Ï€/4

**Answer**

The correct option is C.