Answer
$ \frac{1}{\sqrt (1 - \cos^{2}\theta)}$
Work Step by Step
We know that $\sin\theta$ and $\csc\theta$ are reciprocal to each other-
Therefore-
$\sin\theta\times\csc\theta$ = 1
or $\csc\theta$ = $ \frac{1}{\sin\theta}$
From first Pythagorean identity, we may write $\sin\theta$ as-
$ \sin\theta = ±\sqrt (1 - \cos^{2}\theta)$
Therefore-
$\csc\theta$ = $ \frac{1}{\sqrt (1 - \cos^{2}\theta)}$
