Let x = cos θ

Then, Cos^-1 = θ

Now, R.H.S. = cos^-1(4x³ - 3x)

= cos^-1(4cos³θ - 3cos θ)

= cos^-1(cos3θ)

= 3θ

= 3cos^-1x

= L.H.S.

Hence Proved