Chapter 6 - Analytic Trigonometry - Section 6.7 Product-to-Sum and Sum-to-Product Formulas - 6.7 Assess Your Understanding - Page 524: 5

$\frac{\sqrt 2}{2}$

Use the Sum-to-Product Formula, we have: $cos255^\circ-cos195^\circ=-2sin(\frac{255^\circ+195^\circ}{2}) sin(\frac{255^\circ-195^\circ}{2})=-2sin225^\circ sin30^\circ=2sin45^\circ sin30^\circ=2(\frac{\sqrt 2}{2})(\frac{1}{2})=\frac{\sqrt 2}{2}$