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