Question

How do you express `sin theta - cot theta + tan^2 theta` in terms of `cos theta`?

Answer 1

`(1-cos theta-cos^2 theta)/sqrt(1-cos^2 theta)+1/cos^2 theta-1`

Explanation:

Only Pythagotean identity is used here:
`sin^2 theta+cos^2 theta=1`

`sin theta-cot theta +tan^2 theta=sin theta-cos theta/sin theta+sin^2 theta/cos^2 theta=(sin^2 theta-cos theta)/sin theta+(1-cos^2 theta)/cos^2 theta=(1-cos theta-cos^2 theta)/sqrt(1-cos^2 theta)+1/cos^2 theta-1`

I think it's the simplest form.