# How do you simplify the expression tan(arcsin(x/5)) ?

Aug 1, 2016

$\frac{x}{\sqrt{25 - {x}^{2}}}$

#### Explanation:

Let $a = a r c \sin \left(\frac{x}{5}\right) \in \left[- \frac{\pi}{2} , \frac{\pi}{2}\right]$

Then, $\sin a = \frac{x}{5} \in \left[- 1 , 1\right]$, and so, $x \in \left[- 5 , 5\right]$,

Now, the given expression is

$\tan a$

$= \sin \frac{a}{\cos} a$

$= \sin \frac{a}{\sqrt{1 - {\sin}^{2} a}}$

$= \frac{\frac{x}{5}}{\sqrt{1 - {\left(\frac{x}{5}\right)}^{2}}}$
$= \frac{x}{\sqrt{25 - {x}^{2}}}$