Question

Prove the following: 

3cos^–1x = cos^–1 (4x³ – 3x), `x ∈ [1/2, 1]`

Answer 1

Let x = cos θ.

Then, cos^–1x = θ.

We have,

R.H.S. = cos^–1(4x³ – 3x)

= cos^–1(4 cos³ θ – 3 cos θ)

= cos^–1(cos 3θ)

= 3θ

= 3cos^–1x

= L.H.S.