Question

sin^–1 (1 – x) – 2 sin^–1 x = `pi/2`, then x is equal to ______.

Options

• `0, 1/2`

• `1, 1/2`

• 0

• `1/2`

Answer 1

sin^–1 (1 – x) – 2 sin^–1 x = `pi/2`, then x is equal to 0.

Explanation:

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

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

⇒ 1 – x = cos[cos^–1 (1 – 2x²)]

⇒ 1 – x = 1 – 2x²

⇒ 2x² – x = 0

⇒ `x = 0, 1/2`

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

So, x = 0.