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Trigonometric Ratios and Identities

SSC CGL Quant. Try each one first, then open its answer.

Top 10 SSC CGL PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 22 times: 5 in 2023, 12 in 2024, 5 in 2025. This one: 26 Sep 2025 S1 See all 22 of this type

    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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  2. Question 2

    This type asked 15 times: 21 Jul 2023 S4, 25 Jul 2023 S1, 26 Jul 2023 S2, 27 Jul 2023 S3, 9 Sep 2024 S2, 17 Sep 2024 S3, 12 Sep 2025 S2, 17 Sep 2025 S1, 20 Sep 2025 S1, 21 Sep 2025 S1, 22 Sep 2025 S3, 23 Sep 2025 S1, 24 Sep 2025 S1, 24 Sep 2025 S2, 26 Sep 2025 S3. This one: 26 Sep 2025 S3 See all 15 of this type

    74
    If tan A = 3/4, find sin A.

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  3. Question 3

    This type 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. This one: 26 Sep 2025 S1 See all 12 of this type

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

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  4. Question 4

    This type asked 12 times: 14 Jul 2023 S3, 17 Jul 2023 S2, 18 Jul 2023 S4, 20 Jul 2023 S3, 25 Jul 2023 S3, 26 Jul 2023 S1, 11 Sep 2024 S2, 13 Sep 2024 S1, 13 Sep 2024 S3, 23 Sep 2024 S3, 25 Sep 2024 S3, 21 Sep 2025 S3. This one: 21 Sep 2025 S3 See all 12 of this type

    69
    Find the value of sin⁡290∘+cos⁡260∘\sin^2 90^\circ + \cos^2 60^\circ.

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  5. Question 5

    This type asked 11 times: 18 Jul 2023 S3, 25 Jul 2023 S4, 12 Sep 2024 S3, 24 Sep 2024 S1, 26 Sep 2024 S1, 14 Sep 2025 S3, 23 Sep 2025 S2, 23 Sep 2025 S3, 24 Sep 2025 S3, 26 Sep 2025 S1, 26 Sep 2025 S2. This one: 26 Sep 2025 S2 See all 11 of this type

    72
    If sin⁡x=cos⁡y\sin x = \cos y and cos⁡x=sin⁡y\cos x = \sin y, then x+yx + y equals:

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  6. Question 6

    This type asked 11 times: 14 Jul 2023 S3, 13 Sep 2024 S1, 17 Sep 2024 S1, 18 Sep 2024 S1, 17 Sep 2025 S3, 18 Sep 2025 S3, 19 Sep 2025 S3, 22 Sep 2025 S1, 23 Sep 2025 S3, 24 Sep 2025 S2, 26 Sep 2025 S2. This one: 26 Sep 2025 S2 See all 11 of this type

    69
    If sin⁡A=2x(1+x2)\sin A = \frac{2x}{(1+x^2)}, then what is tan⁡A\tan A in terms of xx?

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  7. Question 7

    This type asked 9 times: 13 Sep 2024 S3, 12 Sep 2025 S2, 14 Sep 2025 S3, 23 Sep 2025 S2, 24 Sep 2025 S1, 24 Sep 2025 S3, 26 Sep 2025 S1, 26 Sep 2025 S2, 26 Sep 2025 S3. This one: 26 Sep 2025 S3 See all 9 of this type

    66
    Convert 3∘3^\circ to radians.

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  8. Question 8

    This type 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. This one: 13 Sep 2024 S2 See all 9 of this type

    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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  9. Question 9

    This type asked 8 times: 17 Jul 2023 S1, 17 Sep 2024 S2, 23 Sep 2024 S2, 17 Sep 2025 S1, 19 Sep 2025 S2, 19 Sep 2025 S3, 21 Sep 2025 S1, 22 Sep 2025 S3. This one: 22 Sep 2025 S3 See all 8 of this type

    68
    If sin⁡A+cos⁡A=22\sin A + \cos A = \frac{\sqrt{2}}{2}, find the value of sin⁡2A+cos⁡2A+2sin⁡Acos⁡A\sin^2 A + \cos^2 A + 2\sin A \cos A.

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  10. Question 10

    This type asked 8 times: 17 Jul 2023 S3, 19 Jul 2023 S2, 27 Jul 2023 S2, 13 Sep 2024 S3, 17 Sep 2024 S2, 23 Sep 2024 S1, 25 Sep 2024 S2, 26 Sep 2024 S3. This one: 26 Sep 2024 S3 See all 8 of this type

    63
    If x=asec⁡θcos⁡ϕ,y=bsec⁡θsin⁡ϕx = a\sec\theta\cos\phi, y = b\sec\theta\sin\phi and z=ctan⁡θz = c\tan\theta, then the value of (x2a2+y2b2−z2c2)\left(\frac{x^2}{a^2} + \frac{y^2}{b^2} - \frac{z^2}{c^2}\right) is equal to:

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