Prove that:

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

Formula Used: cos 3A = 4 cos³ A – 3 cos A

Proof:

LHS = cos^-1 (4x³ – 3x) … (1)

Let x = cos A … (2)

Substituting (2) in (1),

LHS = cos^-1 (4 cos³ A – 3 cos A)

= cos^-1 (cos 3A)

= 3A

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

3A = 3 cos^-1 x

= RHS

Therefore, LHS = RHS

Hence proved.