Use the power-reducing identities to write sin^2xcos^2x in terms of the first power of cosine?

1 Answer
Mar 13, 2018

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

Explanation:

sin^2x=(1-cos(2x))/2

cos^2x=(1+cos(2x))/2

sin^2xcos^2x=((1+cos(2x))(1-cos(2x)))/4=(1-cos^2(2x))/4

cos^2(2x)=(1+cos(4x))/2

(1-(1+cos(4x))/2)/4=(2-(1+cos(4x)))/8=(1-cos(4x))/8