Answer
$6|\tan\theta|$
Work Step by Step
Given expression-
$ \sqrt {x^{2} - 36}$
Substituting $6\sec\theta$ for $x$ as given, the expression becomes-
$ \sqrt {(6\sec\theta)^{2} - 36}$
= $ \sqrt {36\sec^{2}\theta - 36}$
= $ \sqrt {36(\sec^{2}\theta - 1)}$
= $ \sqrt {36\tan^{2}\theta}$
{ Writing $(\sec^{2}\theta - 1)$ as $ \tan^{2}\theta$ from second Pythagorean identity}
= $6|\tan\theta|$
