Answer
Please see below.
Work Step by Step
$$\frac{\sin t + \cos t}{\sec t + \csc t}=\frac{\sin t + \cos t}{\frac{1}{\cos t }+ \frac{1}{\sin t }}= \frac{\sin t + \cos t}{\frac{\sin t + \ cos t }{\cos t \sin t}}=\cos t \sin t= \frac{\sin t }{\sec t}$$
