IMO Shortlist 1966 problem 61


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2. travnja 2012.
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Prove that for every natural number n, and for every real number x \neq \frac{k\pi}{2^t} (t=0,1, \dots, n; k any integer) \frac{1}{\sin{2x}}+\frac{1}{\sin{4x}}+\dots+\frac{1}{\sin{2^nx}}=\cot{x}-\cot{2^nx}
Izvor: Međunarodna matematička olimpijada, shortlist 1966