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Question Id : 16541 | Context : NIMCET 2008
The maximum value of $(\cos\alpha_1)(\cos\alpha_2)\cdots(\cos\alpha_n)$ where $0\le \alpha_1,\alpha_2,\ldots,\alpha_n\le\pi$ and $(\cot\alpha_1)(\cot\alpha_2)\cdots(\cot\alpha_n)=1$ is

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