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tan or cot given: evaluate (a sin + b cos)/(c sin + d cos) by dividing by cos

This type of question, asked 9 times: 19 Jul 2023 S3, 24 Jul 2023 S3, 24 Jul 2023 S4, 26 Jul 2023 S3, 27 Jul 2023 S1, 10 Sep 2024 S2, 10 Sep 2024 S3, 12 Sep 2024 S2, 13 Sep 2024 S2. All 9 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    19 Jul 2023 S3

    74
    If 2cot⁡x=52 \cot x = 5, then what is 2cos⁡x−sin⁡x2cos⁡x+sin⁡x\frac{2 \cos x - \sin x}{2 \cos x + \sin x} equal to?

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  2. Question 2

    24 Jul 2023 S3

    56
    If tan⁡x=75\tan x = \frac{7}{5} ,then the value of 9sin⁡x−425cos⁡x15sin⁡x+21cos⁡x\frac{9\sin x - \frac{42}{5}\cos x}{15\sin x + 21\cos x} is:

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  3. Question 3

    24 Jul 2023 S4

    59
    If acot⁡θ=ba\cot\theta = b, then what will be the value of bcos⁡θ−asin⁡θbcos⁡θ+asin⁡θ\frac{b\cos\theta - a\sin\theta}{b\cos\theta + a\sin\theta} ?

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  4. Question 4

    26 Jul 2023 S3

    58
    If tan⁡A=38\tan A = \frac{3}{8}, then the value of 3sin⁡A+2cos⁡A3sin⁡A−2cos⁡A\frac{3\sin A + 2\cos A}{3\sin A - 2\cos A} is:

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  5. Question 5

    27 Jul 2023 S1

    67
    What is the value of given expression if 3cot⁡A=733\cot A = \frac{7}{3}? 3cos⁡A+2sin⁡A3cos⁡A−2sin⁡A\frac{3\cos A + 2\sin A}{3\cos A - 2\sin A}

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  6. Question 6

    10 Sep 2024 S2

    60
    If 2tan⁡θ=32 \tan \theta = 3, then 3sin⁡θ−2cos⁡θ3sin⁡θ+2cos⁡θ\frac{3 \sin \theta - 2 \cos \theta}{3 \sin \theta + 2 \cos \theta} is equal to:

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  7. Question 7

    10 Sep 2024 S3

    74
    If 7tan⁡θ=37\tan\theta = 3, and θ\theta is an acute angle, then 5sin⁡θ−cos⁡θ5sin⁡θ+2cos⁡θ\frac{5\sin\theta - \cos\theta}{5\sin\theta + 2\cos\theta} is equal to:

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  8. Question 8

    12 Sep 2024 S2

    63
    If 7tan⁡θ=37\tan\theta = 3, then 7sin⁡θ+5cos⁡θ7sin⁡θ−2cos⁡θ\frac{7\sin\theta + 5\cos\theta}{7\sin\theta - 2\cos\theta} is:

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  9. Question 9

    13 Sep 2024 S2

    72
    If tan⁡A=57\tan A = \frac{5}{7}, then find the value of 7sin⁡A−3cos⁡A7sin⁡A+3cos⁡A+4\frac{7\sin A - 3\cos A}{7\sin A + 3\cos A} + 4.

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