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

  $\mathrm{f}$ is a strictly increasing function
• C

  $\mathrm{f}$ is strictly decreasing function
• Correct answer
  D

  $\mathrm{f}$ is a constant function

Hence, the correct answer is option: 'D'.