Answer each of the following questions in one word or one sentence or as per exact requirement of the question:

Show that .

Given LHS = sin^{-1} (2x - √ (1 – x^{2}))

Let x = sin θ

= sin^{-1} (2sin θ √ (1 – sin^{2} θ))

We know that 1 – sin^{2} θ = cos^{2} θ

= sin^{-1} (2 sin θ cos θ)

= sin^{-1} (sin^{2} θ)

= 2θ

= 2 sin^{-1} x

= RHS

∴ sin^{-1} (2x - √ (1 – x^{2})) = 2 sin^{-1} x

1