Answer
$8|\tan\theta|$
Work Step by Step
Given expression-
$ \sqrt {x^{2} - 64}$
Substituting $8\sec\theta$ for $x$ as given, the expression becomes-
$ \sqrt {(8\sec\theta)^{2} - 64}$
= $ \sqrt {64\sec^{2}\theta - 64}$
= $ \sqrt {64(\sec^{2}\theta - 1)}$
= $ \sqrt {64\tan^{2}\theta}$
{ Writing $(\sec^{2}\theta - 1)$ as $ \tan^{2}\theta$ from second Pythagorean identity}
= $8|\tan\theta|$
