Question

What is `cot theta + tan ^2 theta` in terms of `sintheta`?

Answer 1

We know that

`sin^2theta+cos^2theta=1`

`cottheta=costheta/sintheta=(sqrt(1-sin^2theta))/sintheta`

and

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

Hence

`cottheta+tan^2theta=(sqrt(1-sin^2theta))/sintheta+(1-sin^2theta)/(sin^2theta)`