TITLE: Let $f(x) = \arctan x + \mathop{\text{arccot}} x$. Find $f(0) + f(1) + f(\sqrt{2}) + f(\sqrt{3})$.
QUESTION [0 upvotes]: Let $f(x) = \arctan x + \mathop{\text{arccot}} x$. Find $f(0) + f(1) + f(\sqrt{2}) + f(\sqrt{3})$.
This is what i got,
$$\left(0+\frac{\pi}{2}\right)+\left(\frac{\pi}{4}+\frac{\pi}{4}\right)$$

REPLY [1 votes]: Hint. Consider this image:

We know that $\tan \theta = x$, so $\theta = \arctan x$. What is the other angle, as a function of (a) $\theta$ and (b) $x$ ?
{"set_name": "stack_exchange", "score": 0, "question_id": 1313865}