sin4xcos2x / (1+cos4x)(1+cos2x) = ctg ((3pi - 2x )/2) please help this math is killing me?

Answer 1

Note cos 2A = 2 cos^2 A - 1 and sin 2A = 2 sin A cos A. Here we will use A = 2x to get:
LHS = sin 4x cos 2x / [(1+cos 4x)(1+cos 2x)]
= 2 sin 2x cos^2 2x / [(2 cos^2 2x) (1 + cos 2x)]
= sin 2x / (1 + cos 2x)
= 2 sin x cos x / (2 cos^2 x)
= tan x
RHS = cot (3π/2 - x)
= cot (π/2 - x)
= tan x.
So they are equal. 8-)