Question

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

Answer 1

see below

Explanation:

Use the identities:
`sin^2 theta+cos^2 theta = 1`-->solve for `sin^2 theta`
`tan theta = sin theta/ cos theta`
`csc theta=1/sin theta`

Therefore we have to put everything in terms of cosine,
`sin^2 theta - tan theta + csc^2 theta=1-cos^2 theta - sin theta/ cos theta-1/sin^2 theta`

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