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(a sin + b cos)/(c cos + d sin) = k: find cot

The same question, asked 2 times: 14 Jul 2023 S1*, 26 Jul 2023 S2. Every wording 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

    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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