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Trigonometric Ratios and Identities

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

Top 10 SSC CGL Tier II 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 6 times: 15 Nov 2020 Tier II, 29 Jan 2022 Tier II, 3 Feb 2022 Tier II, 8 Aug 2022 Tier II, 2 Mar 2023 Tier II, 18 Jan 2026 Tier II. This one: 18 Jan 2026 Tier II See all 6 of this type

    5
    What is the value of 32(cos⁡39sin⁡51)−sin⁡239∘+sin⁡251∘\frac{3}{2}\left(\frac{\cos 39}{\sin 51}\right) - \sqrt{\sin^2 39^\circ + \sin^2 51^\circ} ?

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  2. Question 2

    This type asked 5 times: 15 Nov 2020 Tier II, 29 Jan 2022 Tier II, 3 Feb 2022 Tier II, 8 Aug 2022 Tier II, 20 Jan 2025 Tier II. This one: 20 Jan 2025 Tier II See all 5 of this type

    6
    Let PQR be a right angled triangle, right-angled at R. Let PQ = 29 cm, QR = 21 cm and ∠Q=θ\angle Q = \theta. Find the value of cos⁡2θ−sin⁡2θ\cos^2\theta - \sin^2\theta.

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  3. Question 3

    This type asked 4 times: 15 Nov 2020 Tier II, 29 Jan 2022 Tier II, 3 Feb 2022 Tier II, 8 Aug 2022 Tier II. This one: 8 Aug 2022 Tier II See all 4 of this type

    36
    Which of the following is equal to [cos⁡θsin⁡θ+sin⁡θcos⁡θ]\left[\frac{\cos\theta}{\sin\theta} + \frac{\sin\theta}{\cos\theta}\right]?

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  4. Question 4

    This type asked 3 times: 15 Nov 2020 Tier II, 20 Jan 2025 Tier II, 18 Jan 2026 Tier II. This one: 18 Jan 2026 Tier II See all 3 of this type

    30
    If sin⁡θx=cos⁡θy\frac{\sin \theta}{x} = \frac{\cos \theta}{y}, then sin⁡θ−cos⁡θ\sin \theta - \cos \theta is:

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  5. Question 5

    This type asked 3 times: 15 Nov 2020 Tier II, 29 Jan 2022 Tier II, 18 Jan 2026 Tier II. This one: 18 Jan 2026 Tier II See all 3 of this type

    17
    Simplify: tan⁡2θ−sin⁡2θ2+tan⁡2θ+cot⁡2θ\frac{\tan^2 \theta - \sin^2 \theta}{2 + \tan^2 \theta + \cot^2 \theta}

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  6. Question 6

    This type asked 3 times: 29 Jan 2022 Tier II, 3 Feb 2022 Tier II, 8 Aug 2022 Tier II. This one: 8 Aug 2022 Tier II See all 3 of this type

    44
    If 3tan⁡θ=3sin⁡θ\sqrt{3}\tan\theta = 3\sin\theta , then what is the value of sin⁡2θ−cos⁡2θ\sin^2\theta - \cos^2\theta?

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  7. Question 7

    Asked 2 times: 29 Jan 2022 Tier II*, 3 Feb 2022 Tier II (* = numbers or wording changed that year) See all 2 times it was asked

    13
    The value of 3(cosec226∘−tan⁡264∘)+(cot⁡242∘−sec⁡248∘)cot⁡(22∘−θ)−cosec2(62∘+θ)−tan⁡(θ+68∘)+tan⁡2(28∘−θ)\frac{3(\text{cosec}^2 26^\circ - \tan^2 64^\circ) + (\cot^2 42^\circ - \sec^2 48^\circ)}{\cot(22^\circ - \theta) - \text{cosec}^2(62^\circ + \theta) - \tan(\theta + 68^\circ) + \tan^2(28^\circ - \theta)} is:

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  8. Question 8

    This type asked 2 times: 3 Feb 2022 Tier II, 18 Jan 2025 Tier II. This one: 18 Jan 2025 Tier II See all 2 of this type

    19
    If sec⁡θ−tan⁡θsec⁡θ+tan⁡θ=19\frac{\sec\theta - \tan\theta}{\sec\theta + \tan\theta} = \frac{1}{9}, θ\theta lies in the first quadrant, then the value of sin⁡θ−tan⁡2θsin⁡θ+tan⁡2θ\frac{\sin\theta - \tan^2\theta}{\sin\theta + \tan^2\theta} is:

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  9. Question 9

    This type asked 2 times: 15 Nov 2020 Tier II, 8 Aug 2022 Tier II. This one: 8 Aug 2022 Tier II See all 2 of this type

    9
    What is the value of 5sin⁡260∘+7sin⁡245∘+8cos⁡245∘5\sin^2 60^\circ + 7\sin^2 45^\circ + 8\cos^2 45^\circ?

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  10. Question 10

    This type asked 2 times: 3 Feb 2022 Tier II, 8 Aug 2022 Tier II. This one: 8 Aug 2022 Tier II See all 2 of this type

    57
    Which of the following is equal to [tan⁡θ+sec⁡θ−1tan⁡θ−sec⁡θ+1]\left[\frac{\tan\theta + \sec\theta - 1}{\tan\theta - \sec\theta + 1}\right] ?

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