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

$-\frac{\sqrt 6}{2}$

Use the Sum-to-Product Formula, we have: $sin255^\circ-sin15^\circ=2sin(\frac{255^\circ-15^\circ}{2}) cos(\frac{255^\circ+15^\circ}{2})=2sin120^\circ cos135^\circ=-2sin60^\circ cos45^\circ=-2(\frac{\sqrt 3}{2})(\frac{\sqrt 2}{2})=-\frac{\sqrt 6}{2}$