# Thread: determine arctan(r) +arctan(s) if r and s are routes of a quadratic equation

1. ## determine arctan(r) +arctan(s) if r and s are routes of a quadratic equation

Hi.

I've encountered this problem and have no idea where to start:

Let r and s be the two solutions to the equation x^2 - 2003x + 2004 = 0. Determine arctan(r) + arctan(s). One is not allowed to use a computer or calculator when solving this, as it was once in a past math competition. Any ideas on how to solve it?

2. ## Re: determine arctan(r) +arctan(s) if r and s are routes of a quadratic equation

Instead of looking directly at $\arctan(r)+\arctan(s),$ I would suggest looking at $\tan\left(\arctan(r)+\arctan(s)\right).$ Start here and also google "properties of roots of quadratic equations." I have debated whether or not to mention the specific result from this search which will be relevant and have decided to leave it out for now; that said, the fact needed will be one of the first results.