Chapter 5 - Section 5.2 - Sum and Difference Formulas - 5.2 Problem Set - Page 289: 53

See the steps.

$\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} $ $\cos{(x-90)} = \cos{x} \times 0 - \sin{x} \times 1 = -\sin{x}$ $LHS = \cos{(x-90)} - \cos{(x+90)} = \sin{x} - (-\sin{x}) = 2 \sin{x}$ $LHS = RHS$