Question 21
Let $a, b, c \in (0, \frac{\pi}{2})$ so that $2(\tan a + \tan b + \tan c) = 3 \tan a \tan b \tan c$.
a) Prove that $\cos^2 a + \cos^2 b + \cos^2 c \ge 1$.
b) Find the minimum for
$$
\frac{1}{\sin^2 a} + \frac{1}{\sin^2 b} + \frac{1}{\sin^2 c}.
$$
a) Prove that $\cos^2 a + \cos^2 b + \cos^2 c \ge 1$.
b) Find the minimum for
$$
\frac{1}{\sin^2 a} + \frac{1}{\sin^2 b} + \frac{1}{\sin^2 c}.
$$