Answer
I know that $\cot$ is an odd function, which means $f(-\theta)=-f(\theta).$ Therefore $\cot{-\theta}=-\cot{\theta}$.
Thus: $1+\cot^2{(-\theta)}=1+(-\cot{(-\theta)})^2=1+\cot^2{\theta}.$
We know that $1+\cot^2{\theta}=\csc^2{\theta}$, hence we proved the identity.
Work Step by Step
I know that $\cot$ is an odd function, which means $f(-\theta)=-f(\theta).$ Therefore $\cot{-\theta}=-\cot{\theta}$.
Thus: $1+\cot^2{(-\theta)}=1+(-\cot{(-\theta)})^2=1+\cot^2{\theta}.$
We know that $1+\cot^2{\theta}=\csc^2{\theta}$, hence we proved the identity.
