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Ratios of one or two angles given: find a double- or compound-angle value

This type of question, asked 3 times: 23 Sep 2024 S1, 18 Sep 2025 S2, 20 Sep 2025 S1. All 3 questions below, oldest first.

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  1. Question 1

    23 Sep 2024 S1

    66
    If 4tan⁡θ−3=04\tan\theta - 3 = 0, then the value of 1−cos⁡2θ1+cos⁡2θ\frac{1 - \cos2\theta}{1 + \cos2\theta} is:

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  2. Question 2

    18 Sep 2025 S2

    64
    If sin⁡A=35\sin A = \frac{3}{5} and cos⁡B=1213\cos B = \frac{12}{13}, AA and B∈(0,π2)B \in \left(0, \frac{\pi}{2}\right), find sin⁡(A+B)\sin(A + B).

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  3. Question 3

    20 Sep 2025 S1

    74
    If sin⁡x=0.6\sin x = 0.6 and x∈(0,π2)x \in \left(0, \frac{\pi}{2}\right), find sin⁡2x+cos⁡2x\sin 2x + \cos 2x.

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