Question

How do you simplify `(csc^2 x - cot^2 x)/secx`?

Answer 1

`cosx`

Explanation:

`(csc^2x-cot^2x)/secx=(1/sin^2x-cos^2x/sin^2x)/(1/cosx)`

`=(1/sin^2x-cos^2x/sin^2x)*cosx`

`=(1-cos^2x)/sin^2x*cosx`

`=cancel(sin^2x)/cancel(sin^2x)*cosx`

`=cosx`