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Find the principal value of each of the following :

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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