# How do you simplify the expression sin(arctan(x/2))?

Jun 4, 2016

$\pm \frac{x}{\sqrt{4 + {x}^{2}}}$

#### Explanation:

Let a = arc tan(x/2). Then, $\tan a = \frac{x}{2}$. As x is a variable, a could be

in any of the four quadrants.,

Accordingly, the given expression

$\sin a = \pm \frac{x}{\sqrt{4 + {x}^{2}}}$