Question

How to prove `sin(4x) = 8 (cos^3)x sin x − 4 cos x sin x`?

Answer 1

`LHS=sin(4x)`

`=2sin2xcos2x`

`=4sinxcosx(2cos^2x-1)`

`= 8 (cos^3)x sin x − 4 cos x sin x=RHS`