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