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