Question

How do you simplify `(secx + cscx)^2cotx`?

Answer 1

`csc^3xsecx(1 + sin2x)`

Explanation:

We have:

`(1/cosx + 1/sinx)^2 * cosx/sinx`

`((sinx + cosx)/(sinxcosx))^2 * cosx/sinx`

`(sin^2x + 2sinxcosx + cos^2x)/(sin^2xcos^2x) * cosx/sinx`

`(1 + 2sinxcosx)/(sin^2xcos^2x) * cosx/sinx`

`(1 + sin2x)/(sin^3xcosx)`

`csc^3xsecx(1 + sin2x)`

Don't know if this simplifies much--hopefully this was the answer you were looking for.