Question:
Find the principal value of each of the following :
$\tan ^{-1}(-1)$
Solution:
$\tan (-1)=-\tan (1)$ [ Formula: $\tan ^{-1}(-x)=-\tan ^{-1}(x)$ ]
[We know that $\tan \frac{\pi}{4}=1$, thus $\tan ^{-1} \frac{\pi}{4}=1$ ]
$=-\frac{\pi}{4}$
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