Question

show sin^2xcos^2x=(1-cos4x)/8

Answer 1

Trig identites

Answer 2

sin^2xcos^2x
= 1/4 (4 sin^2x cos^2x)
= (2sin x cos x)^2 / 4
= (sin2x)^2 / 4
= (1 - 2cos4x)/ 2*4
= (1 - 2cos4x)/ 8