Question

If $\tan^{-1} x$ + $\tan^{-1} y$ = $\frac{2\pi}{3 }$ , then $\cot^{-1} x$ + $\cot^{-1} y$ is equal to

• A. $\frac{\pi }{2 }$
• B. $\frac{ 1}{2 }$
• C. $\frac{\pi }{ 3}$
• D. $\frac{\sqrt{ 3}}{2 }$
• E. $\pi$

Answer 1

Answer: (C)

We have, $\tan ^{-1} x+\tan ^{-1} y=\frac{2 \pi}{3}$
$\Rightarrow \frac{\pi}{2}-\cot ^{-1} x+\frac{\pi}{2}-\cot ^{-1} y=\frac{2 \pi}{3}$
$\Rightarrow \cot ^{-1} x+\cot ^{-1} y=\pi-\frac{2 \pi}{3}=\frac{\pi}{3}$