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Q.
Principal value of $\operatorname{cosec}^{-1}\left(\frac{-2}{\sqrt{3}}\right)$ is equal to
Inverse Trigonometric Functions
Solution:
Let $cosec\,{}^{-1}\left(\frac{-2}{\sqrt{3}}\right)=\theta$
$\Rightarrow cosec\, \theta=\frac{-2}{\sqrt{3}}=-cosec\, \frac{\pi}{3}=cosec\,\left(\frac{-\pi}{3}\right)$
$\Rightarrow \theta=\frac{-\pi}{3} \in\left[\frac{-\pi}{3}, \frac{\pi}{2}\right]-\{0\}$
$\therefore $ Principal value of $cosec\,{}^{-1}\left(\frac{-2}{\sqrt{3}}\right)$ is $\left(\frac{-\pi}{3}\right)$