Q91 / 180 · COMEDK 2020 · Mathematics
The solution of $\tan ^{-1} x+2 \cot ^{-1} x=\frac{2 \pi}{3}$ is
- A$\frac{1}{\sqrt{3}}$
- B$-\frac{1}{\sqrt{3}}$
- Correct answerC$\sqrt{3}$
- D$-\sqrt{3}$
Solution
We have,
$\Rightarrow \tan ^{-1} x+\cot ^{-1} x+\cot ^{-1} x=\frac{2 \pi}{3}$ $\Rightarrow \quad \frac{\pi}{2}+\cot ^{-1} x=\frac{2 \pi}{3}$ $\Rightarrow \quad \cot ^{-1} x=\frac{2 \pi}{3}$ $\Rightarrow \quad \cot ^{-1} x=\frac{\pi}{6}$ $\Rightarrow \quad \cot ^{-1} \frac{\pi}{6}=\sqrt{3}$
Hence, the correct answer is option: 'C'.