PYQ Vault
EbooksTutor

sec + tan = k (or cosec + cot): use sec - tan = 1/k to find a ratio

This type of question, asked 12 times: 14 Jul 2023 S4, 18 Jul 2023 S2, 21 Jul 2023 S1, 24 Jul 2023 S2, 24 Jul 2023 S3, 27 Jul 2023 S2, 9 Sep 2024 S3, 25 Sep 2024 S3, 21 Sep 2025 S2, 23 Sep 2025 S1, 24 Sep 2025 S3, 26 Sep 2025 S1. All 12 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    14 Jul 2023 S4

    63
    If sec⁡θ+tan⁡θ=5\sec\theta + \tan\theta = 5, (θ≠0)(\theta \ne 0), then sec⁡θ\sec\theta is equal to:

    Tap an option to check your answer.

  2. Question 2

    18 Jul 2023 S2

    52
    If sec⁡θ+tan⁡θ=5\sec\theta + \tan\theta = 5, then find the value of tan⁡θ\tan\theta.

    Tap an option to check your answer.

  3. Question 3

    21 Jul 2023 S1

    53
    If sec⁡A+tan⁡A=3\sec A + \tan A = 3, then cos⁡A\cos A is equal to:

    Tap an option to check your answer.

  4. Question 4

    24 Jul 2023 S2

    52
    If Cosec θ+Cot θ=m\text{Cosec}\ \theta + \text{Cot}\ \theta = \text{m}, find the value of m2−1m2+1\frac{m^2 - 1}{m^2 + 1}.

    Tap an option to check your answer.

  5. Question 5

    24 Jul 2023 S3

    72
    If cosec θ+cot⁡θ=32\text{cosec}\,\theta + \cot\theta = \frac{3}{2}, then what is the value of cosec θ\text{cosec}\,\theta?

    Tap an option to check your answer.

  6. Question 6

    27 Jul 2023 S2

    75
    If sec⁡A+tan⁡A=5\sec A + \tan A = 5,then sin⁡A\sin A is equal to:

    Tap an option to check your answer.

  7. Question 7

    9 Sep 2024 S3

    72
    If sec⁡α+tan⁡αsec⁡α−tan⁡α=74\frac{\sec\alpha + \tan\alpha}{\sec\alpha - \tan\alpha} = \frac{7}{4}, then find the value of cosec α\text{cosec}\,\alpha.

    Tap an option to check your answer.

  8. Question 8

    25 Sep 2024 S3

    64
    If sec⁡θ+tan⁡θ=x\sec\theta + \tan\theta = x, then find sin⁡θ\sin\theta.

    Tap an option to check your answer.

  9. Question 9

    21 Sep 2025 S2

    74
    If sec⁡A+tan⁡A=52\sec A + \tan A = \frac{5}{2}, then what is sec⁡A−tan⁡A\sec A - \tan A?

    Tap an option to check your answer.

  10. Question 10

    23 Sep 2025 S1

    67
    If sec⁡A+tan⁡A=p\sec A + \tan A = p, then what is sec⁡A\sec A in terms of p?

    Tap an option to check your answer.

  11. Question 11

    24 Sep 2025 S3

    69
    If sec⁡A−tan⁡A=13\sec A - \tan A = \frac{1}{3}, then what is the value of sec⁡A+tan⁡A\sec A + \tan A?

    Tap an option to check your answer.

  12. Question 12

    26 Sep 2025 S1

    73
    If tan⁡A+sec⁡A=3\tan A + \sec A = 3, find tan⁡A\tan A.

    Tap an option to check your answer.