Prove that cos 4x = 1 – 8sin 2 x cos 2 x

Question

Philoid · Accepted Answer

To prove cos 4x = 1 – 8sin² x cos² x

RHS = 1 – 8sin² x cos² x

LHS = cos 4x

= cos 2(2x)

= 1 – 2 sin² 2x [cos 2A = 1 – 2 sin2 A]

= 1 – 2(2 sin x cos x)²[sin2A = 2sin A cosA]

= 1 – 8 sin² x cos² x

∴ LHS = RHS

Hence, proved.