Q74 / 150 · MHT CET 2021 (20 Sep Shift 2) · Mathematics
$$
\sin ^{-1}\left[\sin \left(-600^{\circ}\right)\right]+\cot ^{-1}(-\sqrt{3})=
$$
- Correct answerA$\frac{\pi}{6}$
- B$\frac{\pi}{4}$
- C$\frac{\pi}{3}$
- D$\frac{7 \pi}{6}$
Solution
$$
\begin{aligned}
& \sin ^{-1}\left[\sin (-600)^{\circ}\right]+\cot ^{-1}(\sqrt{3}) \\
& =\sin ^{-1}\left[-\sin \left(360^{\circ}+180^{\circ}+60^{\circ}\right)\right]+\left[-\cot ^{-1}(\sqrt{3})\right] \\
& =\sin ^{-1}\left[\sin \left(60^{\circ}\right)\right]+\left[-\tan ^{-1}\left(\frac{1}{\sqrt{3}}\right)\right] \\
& =\sin ^{-1}\left[\sin 60^{\circ}\right]-\frac{\pi}{6}=\frac{\pi}{3}-\frac{\pi}{6}=\frac{\pi}{6}
\end{aligned}
$$
Hence, the correct answer is option: 'A'.