To Prove:

Formula Used: sin 2A = 2 × sin A × cos A

Proof:

LHS … (1)

Let x = sin A … (2)

Substituting (2) in (1),

LHS

= sin^-1 (2 × sin A × cos A)

= sin^-1 (sin 2A)

= 2A

From (2), A = sin^-1 x,

2A = 2 sin^-1 x

= RHS

Therefore, LHS = RHS

Hence proved.