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

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–1x = π/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–1x = π/2
Let x = sin y
∴ sin–1(1 − sin y) − 2y = π/2
⇒ sin–1(1 − sin y) = π/2 + 2y
⇒ 1 − sin y = sin (π/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) π/2
(B) π/3
(C) π/4
(D) -3π/4

Answer
The correct option is C.

Exercise 2.1 Inverse Trigonometry

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