Question 21
Suppose $f(x) = a \sin x - \frac{1}{2} \cos 2x + a - \frac{3}{a} + \frac{1}{2}$, $a \in \mathbf{R}$, $a \neq 0$.
(1)
If $f(x) \le 0$ for any $x \in \mathbf{R}$, find the range of $a$.
(2)
If $a \ge 2$ and there exists $x \in \mathbf{R}$ such that $f(x) \le 0$, find the range of $a$.
(1)
If $f(x) \le 0$ for any $x \in \mathbf{R}$, find the range of $a$.
(2)
If $a \ge 2$ and there exists $x \in \mathbf{R}$ such that $f(x) \le 0$, find the range of $a$.