MCQ
Find the principal values of: $\cot ^{-1}(-\sqrt{3})$
- ✓$\frac{5 \pi}{6}$
- B$\frac{\pi}{3}$
- C$\frac{\pi}{2}$
- D$\frac{\pi}{4}$
✓
Answer
Correct option: A.
$\frac{5 \pi}{6}$
(a) : Let $\cot ^{-1}(-\sqrt{3})=\theta \Rightarrow \cot \theta=-\sqrt{3}=-\cot \frac{\pi}{6}$
$=\cot \left(\pi-\frac{\pi}{6}\right)=\cot \frac{5 \pi}{6} \Rightarrow \theta=\frac{5 \pi}{6} \in(0, \pi)$
$\therefore$ Principal value of $\cot ^{-1}(-\sqrt{3})$ is $\frac{5 \pi}{6}$.
$=\cot \left(\pi-\frac{\pi}{6}\right)=\cot \frac{5 \pi}{6} \Rightarrow \theta=\frac{5 \pi}{6} \in(0, \pi)$
$\therefore$ Principal value of $\cot ^{-1}(-\sqrt{3})$ is $\frac{5 \pi}{6}$.
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