Question

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

Answer 1

`(1+costheta-2cos^2theta-cos^3theta)/(costhetasqrt(1-cos^2theta))`

Explanation:

`sintheta-cottheta+tantheta`

= `sintheta-costheta/sintheta+sintheta/costheta`

=`(sin^2thetacostheta-cos^2theta+sin^2theta)/(sinthetaxxcostheta)`

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

=`(1+costheta-2cos^2theta-cos^3theta)/(costhetasqrt(1-cos^2theta))`