Answer
$sin\ u$
Work Step by Step
$\frac{\sqrt(x^2 - 25)}{x}$, $x = 5 sec\ u$
We know that $1 + tan^2\ u=sec^2\ u$, $tan\ u=\frac{sin\ u}{cos\ u}$, and $sec\ u =\frac{1}{cos\ u}$:
$\frac{\sqrt((5 sec\ u)^2 - 25)}{5 sec\ u}=\frac{\sqrt(25 sec^2\ u - 25)}{5 sec\ u}=\frac{5\sqrt( sec^2\ u - 1)}{5 sec\ u}=\frac{\sqrt( tan^2\ u)}{sec\ u}=\frac{tan\ u}{sec\ u}=\frac{sin\ u}{cos\ u}\frac{cos\ u}{1}=sin\ u$
