Let $f(x) = \frac{\sin(x-a) + \sin(x+a)}{\cos(x-a) - \cos(x+a)}$,then
- A$f(x+2\pi) = f(x)$ but $f(x+\alpha) \neq f(x)$ for any $0 < \alpha < 2\pi$
- B$f$ is a strictly increasing function
- C$f$ is a strictly decreasing function
- D$f$ is a constant function
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