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Maximum of a product of cosines under an angle-sum constraint

This type of question, asked 2 times: 16 May 2023 S1, 20 Apr 2025 S1. All 2 questions below, oldest first.

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  1. Question 1

    16 May 2023 S1

    142
    The maximum value of cos⁡α1⋅cos⁡α2⋯cos⁡αn\cos\alpha_1 \cdot \cos\alpha_2 \cdots \cos\alpha_n under the constraints 0≤α1,…,αn≤π20 \leq \alpha_1,\ldots,\alpha_n \leq \frac{\pi}{2} and cot⁡α1⋅cot⁡α2⋯cot⁡αn=1\cot\alpha_1 \cdot \cot\alpha_2 \cdots \cot\alpha_n = 1 is

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  2. Question 2

    20 Apr 2025 S1

    135
    If A+B=π2A+B=\frac{\pi}{2} then the maximum value of cos⁡A⋅cos⁡B\cos A \cdot \cos B is

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