Question 117
Prove that for every real numbers $x_1, x_2, \dots, x_n$, where $n \ge 2$, it is possible to choose $+$ and $-$ so that
$$
\cos (x_1 \pm x_2 \pm \cdots \pm x_n) \le \cos x_1 \cos x_2 \cdots \cos x_n.
$$
$$
\cos (x_1 \pm x_2 \pm \cdots \pm x_n) \le \cos x_1 \cos x_2 \cdots \cos x_n.
$$