Prove that:

To Prove:

Formula Used:

1) cos 2A = 2 cos² A – 1

2)

Proof:

LHS

= cos^-1 (2x² – 1)… (1)

Let x = cos A … (2)

Substituting (2) in (1),

LHS = cos^-1 (2 cos² A – 1)

= cos^-1 (cos 2A)

= 2A

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

2A = 2 cos^-1 x

= RHS

Therefore, LHS = RHS

Hence proved.