Answer
$sec~(cos^{-1}~\frac{u}{\sqrt{u^2+5}}) = \frac{\sqrt{u^2+5}}{u}$
Work Step by Step
Let $~~\theta = cos^{-1}~\frac{u}{\sqrt{u^2+5}}$
Then $~~cos~\theta = \frac{u}{\sqrt{u^2+5}}$
We can find an expression for $sec~\theta$:
$sec~\theta = \frac{1}{cos~\theta}$
$sec~\theta = \frac{\sqrt{u^2+5}}{u}$
Therefore, $~~sec~(cos^{-1}~\frac{u}{\sqrt{u^2+5}}) = \frac{\sqrt{u^2+5}}{u}$
