Question

If ${\tan }^{-1}x+{\tan }^{-1}y=\frac{4\pi }{5}$, then ${\cot }^{-1}x+{\cot }^{-1}y$ is equal to

• A. $\pi$
• B. $\frac{\pi }{5}$
• C. $\frac{2\pi }{5}$
• D. $\frac{3\pi }{5}$

Answer 1

Answer: (B)

We have,
${\tan }^{-1}x+{\tan }^{-1}y=\frac{4\pi }{5}$
$\Rightarrow \frac{\pi }{2}-{\cot }^{-1}x+\frac{\pi }{2}-{\cot }^{-1}y=\frac{4\pi }{5}$
$\Rightarrow {\cot }^{-1}x+{\cot }^{-1}y=\pi -\frac{4\pi }{5}=\frac{\pi }{5}$