$\int \sec \left(x-\frac{\pi}{3}\right) \sec \left(x+\frac{\pi}{6}\right) d x=$

• A

  $\log \left|\frac{\sec \left(x-\frac{\pi}{3}\right)}{\sec \left(x+\frac{\pi}{6}\right)}\right|+c$
• Correct answer
  B

  $\log \left|\frac{\cos \left(x-\frac{\pi}{3}\right)}{\cos \left(x+\frac{\pi}{6}\right)}\right|+c$
• C

  $\log \left|\frac{\operatorname{cosec}\left(x-\frac{\pi}{3}\right)}{\operatorname{cosec}\left(x+\frac{\pi}{6}\right)}\right|+c$
• D

  $\log \left|\frac{\sin \left(x-\frac{\pi}{3}\right)}{\sin \left(x+\frac{\pi}{6}\right)}\right|+c$

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