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a sin + b cos: maximum sqrt(a^2 + b^2), or solve a sin + b cos = c

This type of question, asked 3 times: 18 Sep 2024 S1, 19 Sep 2024 S2, 23 Sep 2024 S1. All 3 questions below, oldest first.

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  1. Question 1

    18 Sep 2024 S1

    62
    If 3sin⁡A+4cos⁡A=53 \sin A + 4 \cos A = 5, then the value of tan⁡A\tan A is:

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  2. Question 2

    19 Sep 2024 S2

    71
    The maximum value of (2sin⁡θ+3cos⁡θ)(2 \sin \theta + 3 \cos \theta) is:

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  3. Question 3

    23 Sep 2024 S1

    71
    The value of θ\theta , when 3cos⁡θ+sin⁡θ=1\sqrt{3}\cos\theta + \sin\theta = 1 (1≤θ≤90∘)(1 \le \theta \le 90^\circ), is:

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