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

Question

Find the principal values:
$\tan^{-1}(-1)$

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Answer

$\text{Let}\ \text{y}=\tan^{-1}\left(-1\right)$, $ \text{where}-\frac{\pi}{2}<\text{Y}<\frac{\pi}{2}$
$\therefore\ \tan\text{y}=-1$, $\text{where}-\frac{\pi}{2}<\text{Y}<\frac{\pi}{2}$
$\therefore\ \ \text{Y}=-\frac{\pi}{4}$, $ \bigg[\because\tan\bigg(-\frac{{\pi}}{4}\bigg)=-\tan\frac{\pi}{4}=-1\bigg]$
$\therefore$ required principal value $=-\frac{\pi}{4}$

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