Answer
$-\sin{x}$
Work Step by Step
Addition formula
$$\sin{(A+B)}= \sin{A} \cos{B} +\cos{A} \sin{B}$$
$\therefore \sin{(2\pi-x)} = \sin{2\pi} \cos{(-x)} + \cos{2\pi} \sin{(-x)}$
$\sin{(2\pi-x)} = (0) \times \cos{x} + (1) \times -\sin{x}$
$\sin{(2\pi-x)} = -\sin{x}$
