# Find the principal values of the following:    3. $\textup{cosec}^{-1}(2)$

D Divya Prakash Singh

Let us assume that $\textup{cosec}^{-1}(2) = x$, then we have;

$Cosec\ x = 2$, or

$Cosec( \frac{\pi}{6}) = 2$  .

And we know the range of principal values is  $[\frac{-\pi}{2},\frac{\pi}{2}] - \left \{ 0 \right \}.$

Therefore the principal value of  $\textup{cosec}^{-1}(2)$ is $\frac{\pi}{6}$.

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