Answer
$ \sin\theta$
Work Step by Step
Given expression is-
$\csc\theta - \cot\theta\cos\theta$
= $\frac{1}{\sin\theta} - \frac{\cos\theta}{\sin\theta}\times\cos\theta$
= $\frac{1}{\sin\theta} - \frac{\cos^{2}\theta}{\sin\theta}$
=$ \frac{1 - \cos^{2}\theta}{\sin\theta} $
= $\frac{\sin^{2}\theta}{\sin\theta}$
[From first Pythagorean identity, $ (1 - \cos^{2}\theta)$ can be written as $\sin^{2}\theta$]
= $ \sin\theta$
