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