Write an equivalent expression for sin^2xcos^2x that does not contain powers of trigonometric functions greater than 1.

Answer 1

Use the half-angle identities sin²x = [1-cos(2x)]/2 and cos²x = [1+cos(2x)]/2:

sin²x·cos²x

= [1-cos(2x)]/2 * [1+cos(2x)]/2

= [1-cos²(2x)]/4

= sin²(2x)/4

= [[1-cos(2(2x))]/2]/4

= [1-cos(4x)]/8

Hope this helped!

Answer 2