Answer
See the explanation below.
Work Step by Step
$\frac{\sin t}{\tan t}+\frac{\cos t}{\cot t}=\sin t+\cos t$
Recall Quotient Identities,
$\begin{align}
& \tan t=\frac{\sin t}{\cos t} \\
& \cot t=\frac{\cos t}{\sin t} \\
\end{align}$
Use the above identities and solve the left side of the given expression,
$\begin{align}
& \frac{\sin t}{\tan t}+\frac{\cos t}{\cot t}=\frac{\sin t}{\frac{\sin t}{\cos t}}+\frac{\cos t}{\frac{\cos t}{\sin t}} \\
& =\sin t\left( \frac{\cos t}{\sin t} \right)+\cos t\left( \frac{\sin t}{\cos t} \right) \\
& =\cos t+\sin t
\end{align}$
Therefore,
$\frac{\sin t}{\tan t}+\frac{\cos t}{\cot t}=\sin t+\cos t$
