# How do you evaluate cos(2 arctan (-2))?

$- \frac{3}{5}$.
Let $a = a r c \tan \left(- 2\right)$. Then, $\tan a = - 2 < 0$. a is in the 2nd quadrant
or in the 4th. So, $\cos a = \pm \frac{1}{\sqrt{5}}$
The given expression is $\cos 2 a = 2 {\cos}^{2} a - 1 = \frac{2}{5} - 1 = - \frac{3}{5}$