Answer
See the steps.
Work Step by Step
$\cos{(x+90)} = \cos{x} \cos{90} -\sin{x} \sin{90} $
$\cos{(x+90)} = \cos{x} \times 0 - \sin{x} \times 1 = -\sin{x}$
$\cos{(x-90)} = \cos{x} \cos{90} + \sin{x} \sin{90} $
$\cos{(x-90)} = \cos{x} \times 0 + \sin{x} \times 1 = \sin{x}$
$LHS = \cos{(x+90)} + \cos{(x-90)} = -\sin{x} + \sin{x} = 0$
$LHS = RHS$