IMO Shortlist 1969 problem 38
Dodao/la:
arhiva2. travnja 2012. ![(HUN 5)](/media/m/f/9/a/f9a7fb480ab565435a090b3d23ba3a57.png)
Let
![r](/media/m/3/d/f/3df7cc5bbfb7b3948b16db0d40571068.png)
and
![m (r \le m)](/media/m/4/8/d/48dfc113fbe306678d55ef45abb976c9.png)
be natural numbers and
![Ak =\frac{2k-1}{2m}\pi](/media/m/9/b/a/9bafd1073c8d21e67ba691b1305249d6.png)
. Evaluate
%V0
$(HUN 5)$ Let $r$ and $m (r \le m)$ be natural numbers and $Ak =\frac{2k-1}{2m}\pi$. Evaluate $\frac{1}{m^2}\displaystyle\sum_{k=1}^{m}\displaystyle\sum_{l=1}^{m}\sin(rA_k)\sin(rA_l)\cos(rA_k-rA_l)$
Izvor: Međunarodna matematička olimpijada, shortlist 1969