Chapter 7 - Analytic Trigonometry - 7.5 Sum and Difference Formulas - 7.5 Assess Your Understanding - Page 488: 71

See below.

$LHS=sin(\alpha-\beta)sin(\alpha+\beta)=[sin(\alpha)cos(\beta)-cos(\alpha)sin(\beta)][sin(\alpha)cos(\beta)+cos(\alpha)sin(\beta)]=sin^2(\alpha)cos^2(\beta)-cos^2(\alpha)sin^2(\beta)=sin^2(\alpha)(1-sin^2(\beta))-(1-sin^2(\alpha))sin^2(\beta)=sin^2(\alpha)-sin^2(\beta)=RHS$