cos^2(x) = 1/2 + (1/2)cos(2x)
sin^2(x) = 1 - cos^2(x) = 1/2 - (1/2)cos(2x)
sin^2(x)cos^2(x)
= [1/2 - (1/2)cos(2x)][1/2 + (1/2)cos(2x)]
(a - b)(a + b) = a^2 - b^2
= (1/2)^2 - (1/2)^2[cos^2(2x)]
= 1/4 - (1/4)cos^2(2x)
= (1/4)[1 - cos^2(2x)]
= (1/4)[sin^2(2x)]
= (1/4)[1/2 - (1/2)cos(4x)]
= (1/4)(1/2)[1 - cos(4x)]
= (1/8)[1 - cos(4x)]
