2. Let $\sin (\alpha+\beta)=\frac{4}{5}, \cos (\alpha-\beta)=\frac{3}{10}$, find the value of $(\sin \alpha-\cos \alpha)(\sin \beta-\cos \beta)$.
$\begin{array}{l}\text { 2. }(\sin \alpha-\cos \alpha)(\sin \beta-\cos \beta) \\ =(\cos \alpha \cdot \cos \beta+\sin \alpha \cdot \sin \beta)- \\ \quad(\sin \alpha \cdot \cos \beta+\cos \alpha \cdot \sin \beta) \\ =\cos (\alpha-\beta)-\sin (\alpha+\beta)=-\frac{1}{2} .\end{array}$