Chapter 6 - Analytic Trigonometry - Section 6.7 Product-to-Sum and Sum-to-Product Formulas - 6.7 Assess Your Understanding - Page 524: 3

$ -\frac{1}{2}(\frac{\sqrt 3}{2}+1)$

$sin285^\circ\cdot sin75^\circ=\frac{1}{2}[cos(285^\circ-75^\circ)-cos(285^\circ+75^\circ)]=\frac{1}{2}[cos(210^\circ)-cos(360^\circ)]=\frac{1}{2}(-\frac{\sqrt 3}{2}-1)=-\frac{1}{2}(\frac{\sqrt 3}{2}+1)$