Find the principal value of: ^ -1 (-1). - Vidyadip

MCQ

Find the principal value of: $\tan ^{-1}(-1)$.

✓
$-\frac{\pi}{4}$
B
$\frac{\pi}{4}$
C
$\frac{\pi}{3}$
D
$\frac{\pi}{6}$

✓

Answer

Correct option: A.

$-\frac{\pi}{4}$

(a): Let $\tan ^{-1}(-1)=x \Rightarrow-1=\tan x$
We know that the range of principal value branch of $\tan ^{-1}$ is $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$.
Then, $-1=\tan \left(-\frac{\pi}{4}\right)$, where $-\frac{\pi}{4} \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$
Hence, the principal value of $\tan ^{-1}(-1)$ is $-\frac{\pi}{4}$.

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