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3 sin t + 5 cos t = c: find 5 sin t - 3 cos t (or 3 cos t - 5 sin t)

The same question, asked 3 times: CDS 2 2018*, CDS 2 2023, CDS 1 2024. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2018

    69
    If 3sin⁡θ+5cos⁡θ=43 \sin \theta + 5 \cos \theta = 4, then what is the value of (3cos⁡θ−5sin⁡θ)2(3 \cos \theta - 5 \sin \theta)^2 ?

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  2. Question 2

    CDS 2 2023

    23
    If 3sin⁡θ+5cos⁡θ=53\sin\theta + 5\cos\theta = 5, then what is the value of 5sin⁡θ−3cos⁡θ5\sin\theta - 3\cos\theta equal to ?

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  3. Question 3

    CDS 1 2024

    32
    If 3sin⁡θ+5cos⁡θ=53 \sin \theta + 5 \cos \theta = 5, then what is the value of 5sin⁡θ−3cos⁡θ5 \sin \theta - 3 \cos \theta ?

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