Find the principal value of ^ -1 (-3) - Vidyadip

MCQ

Find the principal value of $\tan ^{-1}(-\sqrt{3})$

A
$\frac{\pi}{3}$
✓
$-\frac{\pi}{3}$
C
$-\frac{\pi}{6}$
D
$\frac{5\pi}{6}$

✓

Answer

Correct option: B.

$-\frac{\pi}{3}$

b
Let $\tan ^{-1}(-\sqrt{3})=y$

Then, $\tan y=-\sqrt{3}=-\tan \frac{\pi}{3}=\tan \left(-\frac{\pi}{3}\right)$

We know that the range of the principal value branch of $\tan ^{-1}$ is $\left(-\frac{\pi}{2} \frac{\pi}{2}\right)$ and $\tan \left(-\frac{\pi}{3}\right)$ is $-\sqrt{3}$

Therefore, known that the principal value of $\tan ^{-1}(-\sqrt{3})$ is $-\frac{\pi}{3}$

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