$\int_0^{\frac{\pi}{2}} \frac{d x}{\cos x-\sqrt{3} \sin x}=$

• A

  $0$
• B

  $\frac{1}{2} \log (2-\sqrt{3})$
• C

  $\frac{1}{2} \log (2+\sqrt{3})$
• Correct answer
  D

  $\frac{1}{2} \log (2 \sqrt{3}-3)$

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