Answer
See the explanation below.
Work Step by Step
To verify the given identity,
$\csc \theta -\sin \theta =\cot \theta \cos \theta $
Recall Trigonometric Identities,
$\begin{align}
& {{\sin }^{2}}\theta +{{\cos }^{2}}\theta =1 \\
& \cot \theta =\frac{\cos \theta }{\sin \theta } \\
& \csc \theta =\frac{1}{\sin \theta } \\
\end{align}$
Use the above identities and solve the left side of the given expression,
$\begin{align}
& \csc \theta -\sin \theta =\frac{1}{\sin \theta }-\sin \theta \\
& =\frac{1-{{\sin }^{2}}\theta }{\sin \theta } \\
& =\frac{\cos \theta }{\sin \theta }\left( \cos \theta \right) \\
& =\cot \theta \cos \theta
\end{align}$
Hence, it is proved that the given identity holds true.
