# How do you solve Arcsin(x)+arctan(x) = 0?

Apr 7, 2018

$x = 0$

#### Explanation:

We have:

$\arcsin x = - \arctan x$

$\sin x = - \tan x$

$\sin x + \sin \frac{x}{\cos} x = 0$

$\frac{\sin x \cos x + \sin x}{\cos} x = 0$

$\sin x \cos x + \sin x = 0$

$\sin x \left(\cos x + 1\right) = 0$

$\sin x = 0 \mathmr{and} \cos x = - 1$

$x = 0 , \pi$

Since the domain of $\arcsin x$ is -1 ≤ x ≤ 1, the only admissible solution is $x = 0$. The graph confirms:

Hopefully this helps!