Hello

What is

$\displaystyle \mathrm{\lim_{x\rightarrow\frac{\pi}{2}}}\arctan\l eft[C\tan(x)\right]$

where $\displaystyle C$ is a constant. My guess is that it is $\displaystyle -\frac{\pi}{2}$ for $\displaystyle C < 0$ and $\displaystyle \frac{\pi}{2}$ for $\displaystyle C > 0$. However, if this is correct I require more technical treatment.

Many thanks in advance.