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One ratio given as a number: evaluate an expression in the other ratios

This type of question, asked 22 times: 17 Jul 2023 S2, 18 Jul 2023 S1, 19 Jul 2023 S2, 20 Jul 2023 S1, 24 Jul 2023 S1, 9 Sep 2024 S1, 10 Sep 2024 S2, 12 Sep 2024 S3, 13 Sep 2024 S2, 17 Sep 2024 S1, 17 Sep 2024 S3, 18 Sep 2024 S2, 19 Sep 2024 S3, 23 Sep 2024 S3, 24 Sep 2024 S2, 26 Sep 2024 S2, 26 Sep 2024 S3, 17 Sep 2025 S1, 18 Sep 2025 S2, 19 Sep 2025 S1, 21 Sep 2025 S3, 26 Sep 2025 S1. All 22 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    17 Jul 2023 S2

    74
    If Sin θ=45\text{Sin}\,\theta = \frac{4}{5}, find the value of tan⁡θ−Cot θ\tan\theta - \text{Cot}\,\theta.

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  2. Question 2

    18 Jul 2023 S1

    67
    If cot⁡A=125\cot A = \frac{12}{5}, then the value of (sin⁡A+cos⁡A)×cosec A(\sin A + \cos A) \times \text{cosec } A is _______.

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  3. Question 3

    19 Jul 2023 S2

    58
    If sec⁡θ=43\sec\theta = \frac{4}{3}, what is the value of tan⁡2θ+tan⁡4θ\tan^2\theta + \tan^4\theta?

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  4. Question 4

    20 Jul 2023 S1

    54
    If sin⁡x=310\sin x = \frac{3}{10}, then what is the value of tan⁡x+cot⁡x=\tan x + \cot x =?

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  5. Question 5

    24 Jul 2023 S1

    56
    If 2cot⁡θ=32\cot\theta = 3, then find the value of 13sin⁡θ−3tan⁡θ3tan⁡θ+13cos⁡θ\frac{\sqrt{13}\sin\theta - 3\tan\theta}{3\tan\theta + \sqrt{13}\cos\theta}

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  6. Question 6

    9 Sep 2024 S1

    72
    If cosec θ=5/3\text{cosec}\,\theta = 5/3, then evaluate (sec⁡2θ−1)×cot⁡2θ×(1+cot⁡2θ)(\sec^2\theta - 1) \times \cot^2\theta \times (1 + \cot^2\theta).

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  7. Question 7

    10 Sep 2024 S2

    61
    If cot⁡θ=43\cot \theta = \frac{4}{3}, then evaluate sec⁡θ(1+cot⁡2θ)(cosec2θ−cot⁡2θ)cosec3θ\frac{\sec \theta (1 + \cot^2 \theta)(\text{cosec}^2 \theta - \cot^2 \theta)}{\text{cosec}^3 \theta}.

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  8. Question 8

    12 Sep 2024 S3

    74
    If 7cos⁡A=67 \cos A = 6, then the numerical value of cosec⁡A+cot⁡Acosec⁡A−cot⁡A\frac{\operatorname{cosec} A + \cot A}{\operatorname{cosec} A - \cot A} is:

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  9. Question 9

    13 Sep 2024 S2

    65
    If sin⁡B=1517\sin B = \frac{15}{17}, what is the value of cos⁡B(sec⁡B−tan⁡B)\cos B(\sec B - \tan B)? Given that 0<B<π20 < B < \frac{\pi}{2}

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  10. Question 10

    17 Sep 2024 S1

    71
    If sec⁡θ=2920\sec\theta = \frac{29}{20} where 0<θ<90∘0 < \theta < 90^\circ, then what is the value of 3 cosec θ+3cot⁡θ3\,\text{cosec}\,\theta + 3\cot\theta?

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  11. Question 11

    17 Sep 2024 S3

    71
    If cosec x=54\text{cosec}\,x = \frac{5}{4}, then the value of 5sin⁡2x+8cot⁡2x27tan⁡2x−125cos⁡2x\frac{5\sin^2 x + 8\cot^2 x}{27\tan^2 x - 125\cos^2 x} is:

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  12. Question 12

    18 Sep 2024 S2

    71
    If tan⁡θ=815\tan \theta = \frac{8}{15}, and θ\theta is an acute angle, then the value of 1−sin⁡θ1+sin⁡θ\frac{\sqrt{1 - \sin \theta}}{\sqrt{1 + \sin \theta}} is:

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  13. Question 13

    19 Sep 2024 S3

    61
    If tan⁡θ=58\tan \theta = \frac{5}{8}, then find the value of (1+cos⁡θ)(1−cos⁡θ)(1+sin⁡θ)(1−sin⁡θ)\frac{(1 + \cos \theta)(1 - \cos \theta)}{(1 + \sin \theta)(1 - \sin \theta)}.

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  14. Question 14

    23 Sep 2024 S3

    56
    If tan⁡A=110\tan A = \frac{1}{\sqrt{10}}, A is an acute angle, then the value of sin⁡A+cosecA\sin A + \text{cosec} A is:

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  15. Question 15

    24 Sep 2024 S2

    75
    If 3tan⁡A=43 \tan A = 4 and A is an acute angle, then the value of 4sin⁡A+3cos⁡A4\sin A + 3\cos A is:

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  16. Question 16

    26 Sep 2024 S2

    51
    If 8cot⁡θ=78\cot\theta = 7, then the value of 1+sin⁡θcos⁡θ\frac{1 + \sin\theta}{\cos\theta} is:

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  17. Question 17

    26 Sep 2024 S3

    64
    If cot⁡θ=11\cot\theta = \sqrt{11}, then the value of cosec2θ−sec⁡2θcosec2θ+sec⁡2θ\frac{\text{cosec}^2\theta - \sec^2\theta}{\text{cosec}^2\theta + \sec^2\theta} is:

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  18. Question 18

    17 Sep 2025 S1

    65
    What is the value of tan⁡A+cot⁡A\tan A + \cot A if tan⁡A=2\tan A = 2?

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  19. Question 19

    18 Sep 2025 S2

    72
    If cot⁡A=2\cot A = 2, then sin⁡A−cos⁡A=?\sin A - \cos A = ?

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  20. Question 20

    19 Sep 2025 S1

    72
    If sin⁡x=35\sin x = \frac{3}{5} and x∈(0,π/2)x \in (0, \pi/2), then find 1+tan⁡x1−tan⁡x\frac{1 + \tan x}{1 - \tan x}

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  21. Question 21

    21 Sep 2025 S3

    68
    If sin⁡A=110\sin A = \frac{1}{\sqrt{10}}, then find the value of tan⁡A+sec⁡A\tan A + \sec A.

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  22. Question 22

    26 Sep 2025 S1

    65
    If 3cot⁡A=43\cot A = 4, then find the value of (3sin⁡A−4cos⁡A)(3\sin A - 4\cos A).

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