Question

Write the value of ${\sec }^{-1}\left(\frac{1}{2}\right)$.

Answer 1

Given, ${\sec }^{-1}\frac{1}{2}$

Let, ${\sec }^{-1}\frac{1}{2}=\theta$

$\Rightarrow \sec \theta =\frac{1}{2}$

Range of ${\sec }^{-1}$ is $[0,\pi ]-\left\{\frac{\pi }{2}\right\}$

${\sec }^{-1}\frac{1}{2}$ is not in $[0,\pi ]-\left\{\frac{\pi }{2}\right\}$

there is no solution

Hence the solution is $\varphi$