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