Question

Prove that sin 4x =8 cos^3 x sinx - 4 sinx cosx

Answer 1

8 cos³x sinx — 4 sinx cosx
= 4 cos²x (2 sinx cosx) — 2 (2 sinx cosx)
= 4 cos²x sin2x — 2 sin2x
= 2 sin2x ( 2 cos²x — 1 )
= 2 sin2x cos2x
= sin4x