sin2xcos2x Use the power reducing identities to rewrite to a

sin²(x)cos²(x)

Use the power reducing identities to rewrite to an expression that contains a single trigonometric function of power 1

Solution

sin²xcos²x

According to power reducing identities

sin²x= (1-cos2x)/2     and    cos²x=(1+cos2x)/2

therefore sin²xcos²x=(1-cos2x)(1+cos2x)/4= 1/4(1-cos²2x)

applying again power reducing identity

= 1/4((1- (1+cos4x)

=1/8(1-cos4x)