Question 79
Determine all pairs $(x, y)$ of real numbers such that $x, y \in [0, \frac{\pi}{2}]$ for which the following holds:
$$
\frac{2 \sin^2 x + 2}{\sin x + 1} = 3 + \cos (x + y). \quad (\text{Petar Bakić})
$$
$$
\frac{2 \sin^2 x + 2}{\sin x + 1} = 3 + \cos (x + y). \quad (\text{Petar Bakić})
$$