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A linear relation in sin and cos given: find tan or cot (then an expression in it)

This type of question, asked 6 times: 14 Jul 2023 S1, 19 Jul 2023 S1, 26 Jul 2023 S2, 9 Sep 2024 S3, 17 Sep 2024 S3, 14 Sep 2025 S3. All 6 questions below, oldest first.

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  1. Question 1

    14 Jul 2023 S1

    73
    If {(3sin⁡θ−cos⁡θ)/(cos⁡θ+sin⁡θ)}=1\{(3\sin\theta - \cos\theta) / (\cos\theta + \sin\theta)\} = 1, then the value of cot⁡θ\cot\theta is:

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  2. Question 2

    19 Jul 2023 S1

    55
    If sin⁡x−cos⁡xsin⁡x+cos⁡x=25\frac{\sin x - \cos x}{\sin x + \cos x} = \frac{2}{5}, then the value of 1+cot⁡2x1−cot⁡2x\frac{1 + \cot^2 x}{1 - \cot^2 x} is:

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  3. Question 3

    26 Jul 2023 S2

    64
    If 21cos⁡A+3sin⁡A3cos⁡A+4sin⁡A=2\frac{21 \cos A + 3 \sin A}{3 \cos A + 4 \sin A} = 2, then find the value of cot⁡A\cot A

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  4. Question 4

    9 Sep 2024 S3

    64
    If 7sin⁡θ+4cos⁡θ9sin⁡θ−2cos⁡θ=54\frac{7\sin\theta + 4\cos\theta}{9\sin\theta - 2\cos\theta} = \frac{5}{4}, then the value of tan⁡2θ+5tan⁡2θ−5\frac{\tan^2\theta + 5}{\tan^2\theta - 5} is:

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  5. Question 5

    17 Sep 2024 S3

    63
    If sin⁡θ+cos⁡θ=3cos⁡θ\sin\theta + \cos\theta = \sqrt{3}\cos\theta, then the value of cot⁡θ\cot\theta is:

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  6. Question 6

    14 Sep 2025 S3

    75
    If sin⁡A+cos⁡A=2sin⁡A\sin A + \cos A = \sqrt{2}\sin A, then what is the value of tan⁡A\tan A?

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