Answer
Work on the left side of the identity using $\tan{\theta}=\frac{\sin\theta}{\cos\theta}$ and $\sec\theta=\frac{1}{\cos\theta}$..
Refer to the step-by-step part below for the complete proof.
Work Step by Step
We have to show that:
$(\sec\theta+\tan\theta)(\sec\theta-\tan\theta)=1$
By evaluating the left side we get:
$=\sec^2\theta+\sec\theta\tan\theta-\sec\theta\tan\theta-\tan^2\theta\\
=\sec^2\theta-\tan^2\theta$
By using $\sec\theta=\frac{1}{\cos\theta}$ and $\tan\theta=\frac{\sin\theta}{\cos\theta}$, the above expression simpifies to:
$=\dfrac{1}{\cos^2\theta}-\frac{\sin^2\theta}{\cos^2\theta}$
$=\dfrac{1-\sin^2\theta}{\cos^2\theta}$
$=\dfrac{\cos^2\theta}{\cos^2\theta}$
$=1$
Since LHS=RHS, then the identity's proof is complete.