Question:
Find the principal value of $\operatorname{cosec}^{-1}$ (2)
Solution:
Let $\operatorname{cosec}^{-1}(2)=y .$ Then, $\operatorname{cosec} y=2=\operatorname{cosec}\left(\frac{\pi}{6}\right)$
We know that the range of the principal value branch of $\operatorname{cosec}^{-1}$ is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]-\{0\}$.Therefore, the principal value of $\operatorname{cosec}^{-1}$
(2) is $\frac{\pi}{6}$.