Question 81
Let $f$ be a function defined on the set of real numbers $\mathbb{R}$, taking values in $\mathbb{R}$ and satisfying the condition
$$
f(\cot x) = \sin 2x + \cos 2x
$$
for every $x$ belonging to the open interval $(0; \pi)$.
Find the least and the greatest values of the function $g(x) = f(x) \cdot f(1-x)$ on the closed interval $[-1; 1]$.
$$
f(\cot x) = \sin 2x + \cos 2x
$$
for every $x$ belonging to the open interval $(0; \pi)$.
Find the least and the greatest values of the function $g(x) = f(x) \cdot f(1-x)$ on the closed interval $[-1; 1]$.