Answer
The function is even.
Work Step by Step
$f(-x) = \cos{(\sin{(-x)})}$
$\because \sin{(-x)} = -\sin{(-x)} $
$\therefore f(-x) = \cos{(-\sin{x})}$
$\because \cos{(-\theta)} = \cos{\theta}$
$\therefore f(-x) = \cos{(\sin{x})} = f(x)$
The function is even.