Proof:

Take RHS:

{∵ a³ – b³ = (a – b) (a² + b² + ab)}

{∵ cos 2x = cos² x – sin² x}

{∵ a² + b² + 2ab = (a + b)²}

{∵ cos² x + sin² x = 1}

{∵ sin 2x= 2 sin x cos x}

{∵ sin² x = 1 – cos² x}

= LHS

Hence Proved