Question 155
Prove that the inequality
$$
\frac{\cos \alpha}{\sin \alpha} + \frac{\cos \beta}{\sin \beta} + \frac{\cos \gamma}{\sin \gamma} \ge 2
$$
holds for all non-obtuse triangles with angles $\alpha$, $\beta$, $\gamma$ satisfying $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$.
$$
\frac{\cos \alpha}{\sin \alpha} + \frac{\cos \beta}{\sin \beta} + \frac{\cos \gamma}{\sin \gamma} \ge 2
$$
holds for all non-obtuse triangles with angles $\alpha$, $\beta$, $\gamma$ satisfying $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$.