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

Question

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

Philoid · Accepted Answer

Given LHS = sin^-1 (2x - √ (1 – x²))

Let x = sin θ

= sin^-1 (2sin θ √ (1 – sin² θ))

We know that 1 – sin² θ = cos² θ

= sin^-1 (2 sin θ cos θ)

= sin^-1 (sin² θ)

= 2θ

= 2 sin^-1 x

= RHS

∴ sin^-1 (2x - √ (1 – x²)) = 2 sin^-1 x