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Maximum of sin^m + cos^n (powers 2 or more) is 1

This type of question, asked 2 times: 20 Jul 2023 S3, 26 Sep 2024 S3. All 2 questions below, oldest first.

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  1. Question 1

    20 Jul 2023 S3

    66
    The maximum value of (sin⁡12θ+cos⁡20θ)(\sin^{12} \theta + \cos^{20} \theta) for all the real values of θ\theta is:

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  2. Question 2

    26 Sep 2024 S3

    70
    The greatest value of sin⁡4θ+cos⁡4θ\sin^4\theta + \cos^4\theta is:

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