Prove that : 3 sin^(-1)x = sin^(-1)(3x-4x^2)

3 sin^(-1)x = sin^(-1)(3x-4x^2)

Let : sin^(-1)x = y => x= siny = x

Now, sin3y = 3siny- 4sin^3y = 3x-4x^3

Therefore, 3y=sin^(-1)(3x-4x^3)

=> 3sin^(-1)=sin^(-1)(3x-4x^3)

proved.