Question

How do you use the power reducing formulas to rewrite the expression `sin^2xcos^2x` in terms of the first power of cosine?

Answer 1

`(1 - cos 4x)/8`

Explanation:

Use trig identites:
sin 2x = 2sin x.cos x
`2sin^2 x = 1 - cos 2x`
In this case, we have:
`sin^2 x.cos^2 x = (sin^2 2x)/4`
Substitute `sin^2 2x` by `(1 - cos 4x)/2`

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