Question

Principal value of ${\sec }^{-1}(2)$ is equal to

• A. $\frac{\pi }{6}$
• B. $\frac{\pi }{3}$
• C. $\frac{2\pi }{3}$
• D. $\frac{5\pi }{3}$

Answer 1

Answer: (B)

Let ${\sec }^{-1}(2)=\theta$
$\Rightarrow \sec \theta =2=\sec \frac{\pi }{3}$
$\Rightarrow \theta =\frac{\pi }{3}\in [0,\pi ]-\left\{\frac{\pi }{2}\right\}$
$\therefore$ Principal value of ${\sec }^{-1}(2)$ is $\frac{\pi }{3}$