Answer
$-\cos{x}$
Work Step by Step
Addition formula
$$\cos{(A+B)}= \cos{A} \cos{B}-\sin{A}\sin{B}$$
$\therefore \cos{(\pi+x)} = \cos{\pi} \cos{x} - \sin{\pi} \sin{x}$
$\cos{(\pi+x)} = (-1) \times \cos{x} - (0) \times \sin{x}$
$\cos{(\pi+x)} = -\cos{x}$
