Answer
See the explanation below.
Work Step by Step
The given expression on the left side $\frac{\sec t-1}{t\sec t}$ can be further simplified by multiplying and dividing by $\cos t$.
$\begin{align}
& \frac{\sec t-1}{t\sec t}=\frac{\sec t-1}{t\sec t}.\frac{\cos t}{\cos t} \\
& =\frac{\sec t.\cos t-\operatorname{cost}}{t\sec t.\cos t}
\end{align}$
Now, the expression can be further simplified by using the reciprocal identity $\sec t=\frac{1}{\cos t}$
$\begin{align}
& \frac{\sec t.\cos t-\operatorname{cost}}{t\sec t.\cos t}=\frac{\frac{1}{\cos t}.\cos t-\cos t}{t\sec t.\cos t} \\
& =\frac{1-\cos t}{t}
\end{align}$
Hence, the left side is equal to the right side $\frac{\sec t-1}{t\sec t}=\frac{1-\cos t}{t}$.
