Question

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

Answer 1

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

Explanation:

`sin^2theta-cottheta+tan^2theta` can be written as

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

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

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