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

Question

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

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Answer

$\text{Let cosec}^{-1}(-\sqrt{2})=\text{y}$
$-\sqrt{2}=\text{cosec y}-\text{cosec}\frac{\pi}{4}=\text{cosec y}$
$\text{Hence y}=-\frac{\pi}{4}$

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