If $\cot \frac{x}{2}-\operatorname{cosec} \frac{x}{2}=\cot x$, then the values of $x$ are

• A

  $2 n \pi$
• Correct answer
  B

  $4 n \pi \pm \frac{2 \pi}{3}$
• C

  $2 n \pi \pm \frac{\pi}{3}$
• D

  $n \pi$

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