Proof:

Take LHS:

Identities used:

cos 2x = 1 – 2 sin² x

⇒ 2 sin² x = 1 – cos 2x

Therefore,

{∵ cos (π – θ) = - cos θ,

cos (π + θ) = - cos θ &

cos(2π – θ) = cos θ}

= 2

= RHS

Hence Proved