Answer
$\sin{x}$
Work Step by Step
Addition formula
$$\cos{(A+B)}= \cos{A} \cos{B}-\sin{A}\sin{B}$$
$\therefore \cos{\left(\dfrac{3\pi}{2}+x \right)} = \cos{\left(\dfrac{3\pi}{2} \right)} \cos{x} - \sin{\left(\dfrac{3\pi}{2} \right)} \sin{x}$
$ \cos{\left(\dfrac{3\pi}{2}+x \right)} = (0) \times \cos{x} - (-1) \times \sin{x}$
$ \cos{\left(\dfrac{3\pi}{2}+x \right)} = \sin{x}$
