Question

Find the value of $2{\sec }^{-1}2+{\sin }^{-1}\left(\frac{1}{2}\right)$

Answer 1

$$\begin{gathered} 2{\sec }^{-1}2+{\sin }^{-1}\left(\frac{1}{2}\right)=2{\sec }^{-1}\left(\sec \frac{\mathrm{\pi }}{3}\right)+{\sin }^{-1}\left(\sin \frac{\mathrm{\pi }}{6}\right) \\ =2\times \frac{\mathrm{\pi }}{3}+\frac{\mathrm{\pi }}{6} \\ =\frac{5\mathrm{\pi }}{6} \end{gathered}$$