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Prove that the maximum value of (cos alp...

Prove that the maximum value of `(cos alpha_(1)) (cos alpha_(2))...( cos alpha_(r))` uder the restrictions `0 le alpha_(r) le (pi)/(2) (r=1, 2,..., n) and (cot alpha_(1)) (cot alpha_(2))...( cot alpha_(r))=1 "is" (1)/(2^(n/2))`

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