Prove that for every natural number , and for every real number (; any integer)
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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
Školjka 
, and for every real number 
(
; 
any integer) 