Question

How do you verify `(1-cos^2x)(1+cos^2x)=2sin^2x-sin^4x`?

Answer 1

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

Explanation:

Replace `( 1 - cos^2 x)` by `sin^2 x` and `cos^2 x` by `1 -sin^2 x`, we get:
`(1 - cos ^2 x) (1 + cos^2 x)` =
`sin^2 x ( 1 + 1 - sin^2 x)`=
`sin^2 x (2 - sin^2 x) = 2sin ^2 x - sin^4 x`