1. cos 4x= 1-8sin²x cos²x

Right Side = 1 - 2 (4sin²x cos²x) = 1 - 2 (2sin x . cos x)²

= 1 - 2 (sin 2x)² = (1)- 2 sin² 2x = (sin² 2x + cos² 2x) -2sin² 2x

= cos² 2x - sin² 2x = cos 4x

2. (sin³x - cos³x)/(sinx - cosx) = 1+sinxcosx

Left side

because