Maximum Value of trig

Geometry Level 3

\[\large \prod_{m=1}^n \cos(A_m) \]

For angles \(0\leq A_1,A_2,A_3,\ldots ,A_n\leq 90^\circ \), find the maximum value of the product above with the restriction of \( \displaystyle \prod_{m=1}^n \cot(A_m) = 1 \).

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