402. Simplify the expression

$$
\frac{\cos \alpha \cos \beta-\cos (\alpha+\beta)}{\cos (\alpha-\beta)-\sin \alpha \sin \beta}
$$
Solution. Applying formulas (5) and (6), we get

$$
\begin{gathered}
\frac{\cos \alpha \cos \beta - \cos (\alpha + \beta)}{\cos (\alpha - \beta) - \sin \alpha \sin \beta} = \frac{\cos \alpha \cos \beta - \cos \alpha \cos \beta + \sin \alpha \sin \beta}{\cos \alpha \cos \beta + \sin \alpha \sin \beta - \sin \alpha \sin \beta} = \\
= \frac{\sin \alpha \sin \beta}{\cos \alpha \cos \beta} = \operatorname{tg} \alpha \operatorname{tg} \beta
\end{gathered}
$$