#### 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

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

(B) 1, 1/2

(C) 0Â

(D) 1/2

Answer

Given that sin

^{â€“1}(1 âˆ’ x) âˆ’ 2sin^{â€“1}x = Ï€/2
Let x = sin y

âˆ´ sin

^{â€“1}(1 âˆ’ sin y) âˆ’ 2y = Ï€/2
â‡’ sin

^{â€“1}(1 âˆ’ sin y) = Ï€/2 + 2y
â‡’ 1 âˆ’ sin y = sin (Ï€/2 + 2y)

â‡’ 1 âˆ’ sin y = cos 2y

â‡’ 1 âˆ’ sin y = 1 âˆ’ 2sin

^{2}y [as cos^{2}y = 1âˆ’2sin^{2}y]
â‡’ 2sin

^{2}y âˆ’ sin y = 0
â‡’ 2x

^{2}Â âˆ’ x = 0 [as x = sin y]
â‡’ x(2x âˆ’ 1) = 0

â‡’ x = 0 or,Â x = 1/2

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

âˆ´ x = 0 is the solution of the given equation.

The correct option is C.

Question: 17

tan

^{â€“1}(x/y) âˆ’Â tan^{â€“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.