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