#### 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

Question: 2

Prove that

Question: 3

Question: 4

Question: 5

Question: 6

Question: 7

Question: 8

Page No. 52

Prove that

Question: 9

Question: 10

Question: 11

Question: 12

Solve the following equations:

Question: 13

Question: 14

Question: 15

The correct option is D.

Question: 16
sin–1(1 – x) – 2 sin–1x = Ï€/2, then x is equal to
(A) 0, 1/2
(B) 1, 1/2
(C) 0
(D) 1/2

Given that sin–1(1 − x) − 2sin–1x = 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 − 2sin2y [as cos2y = 1−2sin2y]
⇒ 2sin2y − sin y = 0
⇒ 2x2 − 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