Find the principal values: cosec^ -1 (2) - Vidyadip

Question

Find the principal values:
$\text{cosec}^{-1}(2)$

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Answer

$\text{Let y}==\text{cosec}^{-1}(2)$, $\text{where}\ \text{y}\in\bigg[\frac{-\pi}{2},0\bigg]\cup\bigg(0,\frac{{\pi}}{2}\bigg)$
$\therefore\ \ \text{cosec y}=2$, $\text{where y}\in\bigg[\frac{-\pi}{2},0\bigg]\cup\bigg(0,\frac{\pi}{2}\bigg)$
$\therefore\text{Y}=\frac{\pi}{6}$
$\therefore$ required principal value $ =\frac{\pi}{6}$

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