Prove the following identities:
cos3 2x + 3 cos 2x = 4(cos6 x – sin6 x)
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