Question 13
Let $a$ be a real number. Prove that there exist real numbers $b$ and $c$ such that the inequalities
$$ \min \{\sin(x), \sin(a+x)\} \le b \sin(x+c) \le \max \{\sin(x), \sin(a+x)\} $$
hold for all real numbers $x$ and the equalities hold only if $\sin(x) = \sin(a+x)$.
$$ \min \{\sin(x), \sin(a+x)\} \le b \sin(x+c) \le \max \{\sin(x), \sin(a+x)\} $$
hold for all real numbers $x$ and the equalities hold only if $\sin(x) = \sin(a+x)$.