Answer
Identity proved.
Work Step by Step
In order to prove the given identity, we simplify the left hand side $\text{LHS}$.
We know that $\cos \theta =\dfrac{1}{\sec \theta}$
$\text{LHS } =\dfrac{\dfrac{1}{\sec \theta} +1}{\dfrac{1}{\sec \theta} -1} \\=\dfrac{\dfrac{1+\sec \theta}{\sec \theta}}{\dfrac{1-\sec \theta }{\sec \theta}} \\= \dfrac{1+\sec \theta}{1-\sec \theta} \\= \text{ RHS}$
Thus the left-hand side equals the right-hand side and we have proven the identity.
