Question

The number of solutions of sin^–1x + sin^–1(1 – x) = cos^–1x is

Options

• 1

• 0

• 2

• 4

Answer 1

2

Explanation:

sin^–1x + sin^–1(1 – x) = cos^–1x = `pi/2 - 2sin^(-1)x`

⇒ `1 - x = cos(2sin^(-1)x) = 1 - 2(sin^(-1)x)^2 = 1 - 2x^2`

⇒ `2x^2 - x` = 0

⇒ x = 0 or `1/2`