Question 100
If $(ABC)$ denotes the area of $ABC$ prove that
$$
(ABC) = \frac{a^2}{2(\cot B + \cot C)}.
$$
Deduce or prove otherwise that if $ABC$ is acute-angled, then
$$
\cos A \cos B \cos C \le \frac{1}{8},
$$
with equality iff the triangle is equilateral.
$$
(ABC) = \frac{a^2}{2(\cot B + \cot C)}.
$$
Deduce or prove otherwise that if $ABC$ is acute-angled, then
$$
\cos A \cos B \cos C \le \frac{1}{8},
$$
with equality iff the triangle is equilateral.