Prove the identity. 3 sin(4x)/ sin(x) = 12 cos(x) cos(2x)

Answer 1

Recall that sin(2θ) = 2sinθcosθ

So, 3sin(4x) / sinx = 3(2sin(2x)cos(2x)) / sinx = 6sin(2x)cos(2x) / sinx = 6(2sinxcosx)cos(2x) / sinx

= 12cos(2x)cosx