Question

How do you simplify `cos^2x(sec^2x-1)`?

Answer 1

`sin^2x`.

Explanation:

Rewrite `sec^2x` as `1/cos^2x` by the identity `secx = 1/cosx`.

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

`= 1 - cos^2x`

Use the identity `sin^2x + cos^2x = 1` solved for `sin^2x` to get:

`= sin^2x`

Hopefully this helps!