Question

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

Answer 1

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

Explanation:

`sintheta= sqrt(1-cos^2theta`
`cottheta=costheta/sintheta=costheta/sqrt(1-cos^2theta`
`tan^2theta= sec^2theta - 1=1/(cos^2theta) - 1` = `{1-cos^2theta}/cos^2theta`

Hence, the reqd. expression =`sqrt(1-cos^2theta` -- `costheta/sqrt(1-cos^2theta`+`(1 -cos^2theta)/cos^2theta`