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