IMO 1969 LL HUN38

Let r and m (r \leqm) be natural numbers and Ak = 2k−1

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IMO 1969 LL HUN38

Origin: HUN

Problem

Let r and m (r \leqm) be natural numbers and Ak = 2k−1 2m \pi. Evaluate m2 m  k=1 m  l=1 sin(rAk) sin(rAl) cos(rAk −rAl).