Question 1
Write $\mathbb R$ for the set of real numbers. A function $f:\mathbb R\to\mathbb R$ satisfies
$$f(\cot x)=\cos2x+\sin2x$$
for every $0\lt x\lt \pi$. Determine $g(x)=f(x)f(1-x)$ for $-1\le x\le1$. Find the maximum and minimum values of $g(x)$ on $[-1,1]$.
$$f(\cot x)=\cos2x+\sin2x$$
for every $0\lt x\lt \pi$. Determine $g(x)=f(x)f(1-x)$ for $-1\le x\le1$. Find the maximum and minimum values of $g(x)$ on $[-1,1]$.