Question 84
Let $\alpha$ and $\beta$, $\alpha \neq \beta$, be acute angles such that
$$
(\cos^2 \alpha + \cos^2 \beta)(1 + \tan \alpha \tan \beta) = 2.
$$
Prove that $\alpha + \beta = 90^\circ$.
$$
(\cos^2 \alpha + \cos^2 \beta)(1 + \tan \alpha \tan \beta) = 2.
$$
Prove that $\alpha + \beta = 90^\circ$.