How can I prove that $\operatorname{arctg}(x) + \operatorname{arctg}(\frac{1}{x}) = \frac{\pi}{2}$, given that $x > 0$? – math.stackexchange...

How can I prove that $\operatorname{arctg}(x) +
\operatorname{arctg}(\frac{1}{x}) = \frac{\pi}{2}$, given that $x > 0$? –
math.stackexchange...

Which would be the easier way to prove that $\operatorname{arctg}(x) +
\operatorname{arctg}(\frac{1}{x}) = \frac{\pi}{2}$ in cases where $x > 0$?
I don't need explicit solutions, rather keywords …