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Maximum of a trig expression on [0, pi]

This type of question, asked 2 times: 13 Apr 2023, 4 Apr 2026 S2. All 2 questions below, oldest first.

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  1. Question 1

    13 Apr 2023

    62
    max⁡0≤x≤π{x−2sin⁡xcosx+13sin⁡3x}=\underset{0 \leq x \leq \pi}{\max} \left\{ x - 2\sin xcosx +\frac{1}{3}\sin3x \right\}=

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  2. Question 2

    4 Apr 2026 S2

    62
    max⁡0≤x≤π(16sin⁡(x2)cos⁡3(x2))\max_{0 \leq x \leq\pi} \left( 16\sin\left( \frac{x}{2} \right)\cos^{3}\left( \frac{x}{2} \right) \right) is equal to :

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