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