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} $