Answer
The expression on the left side is equal to the expression on the right side.
Work Step by Step
We have the expression on the left side $\left( \sec \theta -1 \right)\left( \sec \theta +1 \right)={{\sec }^{2}}\theta -1$ and using the identity ${{\sec }^{2}}\theta ={{\tan }^{2}}\theta +1$ we simplify as:
$\begin{align}
& \left( \sec \theta -1 \right)\left( \sec \theta +1 \right)={{\sec }^{2}}\theta -1 \\
& =1+{{\tan }^{2}}\theta -1 \\
& ={{\tan }^{2}}\theta
\end{align}$
Hence, the expression on the left side is equal to the expression on the right side $\left( \sec \theta -1 \right)\left( \sec \theta +1 \right)={{\tan }^{2}}\theta $.
