Question

If sin^–1(1 – x) – 2sin^–1x = (π/2) then x = __________

(a) 0, (1/2)

(b) 1, (1/2) 

(c) 0 

(d) (1/2)

Answer 1

The correct option  (c) 0 

Explanation:

given: sin^–1(1 – x) – 2 sin^–1x = (π/2)

∴ sin^–1(1 – x) = (π/2) + 2 sin^–1x

∴ (1 – x) = sin[(π/2) + 2 sin^–1x] 

∴ (1 – x) = cos(2 sin^–1x) 

Let θ = sin^–1x ⇒ sin θ = x

∴ 1 – x = cos2θ = 1 – 2 sin²θ

∴ 1 – x = 1 – 2x² 

∴ 2x² – x = 0

∴ x(2x – 1) = 0 

⇒ x = 0 or x = (1/2)

as x = (1/2) does not satisfy equation

 ∴ x = 0.