$\frac{\sin \alpha \sin (\alpha+\beta)+\cos \alpha \cos (\alpha+\beta)}{\cos \beta}=?$
$$
\begin{gathered}
\frac{\sin \alpha \sin (\alpha+\beta)+\cos \alpha \cos (\alpha+\beta)}{\cos \beta}= \\
\frac{\sin ^{2} \alpha \cos \beta+\sin \alpha \cos \alpha \sin \beta+\cos ^{2} \alpha \cos \beta-\cos \alpha \sin \alpha \sin \beta}{\cos \beta}= \\
=\frac{\sin ^{2} \alpha \cos \beta+\cos ^{2} \alpha \cos \beta}{\cos \beta}=\sin ^{2} \alpha+\cos ^{2} \alpha=1
\end{gathered}
$$

(Dezső Szöke, Zenta.)

Number of solutions: 22.