At which point does this curve y = cot^-1 x meet the curve y = tan^-1 x?

Explanation

1. 01

   At a common point $\tan^{-1} x = \cot^{-1} x = \theta$, so $\tan \theta = x = \cot \theta$ and $\tan^{2} \theta = 1$.

2. 02

   $\theta$ lies in both branches, so in $\left(0, \frac{\pi}{2}\right)$: $\theta = \frac{\pi}{4}$ and $x = 1$.