Prove that : 3 sin^–1x = sin^–1 (3x – 4x³), x ∈ .

To Prove: 3 sin^–1x = sin^–1 (3x – 4x³)

Proof: 

we know that,

sin3θ = 3 sinθ - 4 sin³θ.....(1)

Let sinθ = x, then

θ = sin^-1 x

Put the value in equation 1, we get,

sin3θ = 3x - 4x³

3θ = sin^-1(3x - 4x³)

3 sin^–1x = sin^–1 (3x – 4x³)

Hence, Proved.