I understand how it works when it is sin^2 x cos^2 x but I do not know what to do when I am given a 2x.

Hello Angel, a fellow El Pasoan.

Using the identities

sin

^{2}u = (1-cos(2u))/2cos

^{2}u = (1+cos(2u))/2In this case, we can make it so that u=2x. This is the value that is doubled in the identity.

sin

^{2}(2x)cos^{2}(2x)= ((1-cos(4x))/2)((1+cos(4x))/2)

= (1-cos

^{2}(4x))/4We can take it a step further to get it to the first power.

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

= (2/2-(1-cos(8x))/2)/4 Common demoninator

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

= (1+cos(8x))/8