Answer
See the explanation below.
Work Step by Step
$\frac{{{\csc }^{2}}t}{\cot t}=\csc t\sec t$
Recall Trigonometric Identities,
$\begin{align}
& \csc t=\frac{1}{\sin t} \\
& \sec t=\frac{1}{\cos t} \\
& \cot t=\frac{\cos t}{\sin t} \\
\end{align}$
Use the above identities and solve the left side of the given expression,
$\begin{align}
& \frac{{{\csc }^{2}}t}{\cot t}=\frac{\frac{1}{{{\sin }^{2}}t}}{\frac{\cos t}{\sin t}} \\
& =\frac{1}{{{\sin }^{2}}t}\cdot \frac{\sin t}{\cos t} \\
& =\frac{1}{\sin t}\cdot \frac{1}{\cos t} \\
& =\csc t\sec t
\end{align}$
Therefore,
$\frac{{{\csc }^{2}}t}{\cot t}=\csc t\sec t$
