Answer:
Option A
Explanation:
$\int \frac{dx}{\cos x+\sqrt{3}sin x}$
= $\frac{1}{2}\int \frac{dx}{\frac{1}{2}\cos x+\frac{\sqrt{3}}{2}sin x}$
=$\frac{1}{2}\int \frac{dx}{\cos\frac{\pi}{3}\cos x+\sin\frac{\pi}{3}sin x}$
= $\frac{1}{2}\int \frac{dx}{\cos(x-\frac{\pi}{3})}$
=$\frac{1}{2}\int \sec (x-\frac{\pi}{3}) dx$
=$\frac{1}{2}\log \tan (\frac{x}{2}-\frac{\pi}{6}+\frac{\pi}{4})+C$
= $\frac{1}{2}\log \tan (\frac{x}{2}+\frac{\pi}{12})+C$
