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