Chapter 6 - Analytic Trigonometry - Section 6.7 Product-to-Sum and Sum-to-Product Formulas - 6.7 Assess Your Understanding - Page 524: 1

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

Use the Product-to-Sum formula, we have: $sin195^\circ\cdot cos75^\circ=\frac{1}{2}[sin(195^\circ+75^\circ)+sin(195^\circ-75^\circ)]=\frac{1}{2}[sin(270^\circ)+sin(120^\circ)]=\frac{1}{2}[-1+\frac{\sqrt 3}{2}] =\frac{1}{2}(\frac{\sqrt 3}{2}-1) $