Question

How do you prove `sin8x = 8sinx cosx cos2x cos4x`?

Answer 1

Apply the 2 trig identity: sin 2a = 2sin a.cos a
sin 8x = 2sin 4x.cos 4x
Since sin 4x = 2sin 2x.cos 2x, therefor,
sin 8x = 2(2sin 2x.cos 2x)cos 4x =
Since sin 2x = 2sin x.cos x, therefor,
sin 8x = 4(2sin x.cos x).cos 2x.cos 4x.
sin 8x = 8sin x.cos x.cos 2x.cos 4x