Question 10
Let $a$ and $b$ be the lengths of the legs of a given right triangle. Prove that angle $\varphi$, where $0 \lt \varphi \lt 90^\circ$, is an acute angle of this triangle if and only if $(a \cos \varphi + b \sin \varphi)(a \sin \varphi + b \cos \varphi) = 2ab$. (Seniors.)