Question

The value of ${\sec }^{-1}\left(\text{cosec}\frac{11\pi }{3}\right)$ is

• A. $\frac{11\pi }{3}$
• B. $\frac{11\pi }{6}$
• C. $\frac{5\pi }{6}$
• D. $\frac{7\pi }{6}$

Answer 1

The correct option is C $\frac{5\pi }{6}$

${\sec }^{-1}\left(\text{cosec}\frac{11\pi }{3}\right)=\frac{\pi }{2}-{\text{cosec}}^{-1}\left(\text{cosec}(4\pi -\frac{\pi }{3})\right)=\frac{\pi }{2}-(-\frac{\pi }{3})=\frac{5\pi }{6}$