is my answer wrong?
Maximum value of
\cos(\alpha_1)\cos(\alpha_2)...\cos(\alpha_n) under the restrictions 0\leq \alpha_1, \alpha_2, .....\alpha_n \leq \pi/2 and cot(\alpha_1)cot(\alpha_2) .....cot(\alpha_n) = 1
is?
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3 Answers
Optimus Prime
·2009-03-21 09:22:18
i will call alpha as A
cotA1.cotA2.........cotAn=1
cosA1.cosA2,......cosAn=sinA1..........sinAn=X
X2=(cosA1.cosA2....cosAn)(sinA1.sinA2....sinAn)
= 1/2n(sin2A1)(sin2A2)....(sin2An)
X2≤1/2n since sin2A1≤1
X≤1/2n/2
hence maximum value of given expression is 1/2n/2