Proof:

Take LHS:

Identities used:

cos 2x = 2 cos² x – 1

⇒ 2 cos² x = 1 + cos 2x

Therefore,

{∵ cos (π – θ) = - cos θ, cos (π + θ) = - cos θ & cos(2π – θ) = cos θ}

= 2

= RHS

Hence Proved