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Trigonometric Ratios and Identities

CDS Maths. Try each one first, then open its answer.

Top 10 CDS 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 8 times: CDS 2 2017, CDS 2 2018, CDS 2 2019, CDS 1 2020, CDS 2 2021, CDS 2 2022, CDS 1 2023, CDS 2 2025. This one: CDS 2 2025 See all 8 of this type

    35
    If cot⁡θ=7\cot\theta = \sqrt{7}, then what is cosec2θ−sec⁡2θcosec2θ+sec⁡2θ\dfrac{\mathrm{cosec}^2\theta - \sec^2\theta}{\mathrm{cosec}^2\theta + \sec^2\theta} equal to?

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  2. Question 2

    This type asked 7 times: CDS 2 2016, CDS 1 2018, CDS 2 2020, CDS 1 2025, CDS 2 2025, CDS 1 2026, CDS 2 2026. This one: CDS 2 2026 See all 7 of this type

    49
    If (cos⁡35∘+cos⁡55∘)=p(\cos 35^\circ + \cos 55^\circ) = p, then what is sin⁡35∘⋅cos⁡35∘\sin 35^\circ \cdot \cos 35^\circ equal to ?

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  3. Question 3

    This type asked 6 times: CDS 2 2021, CDS 1 2022, CDS 1 2023, CDS 2 2023, CDS 1 2025, CDS 2 2025. This one: CDS 2 2025 See all 6 of this type

    33
    If 2tan⁡θ=sec⁡2θ−22\tan\theta = \sec^2\theta - 2, where 0<θ<π/20 < \theta < \pi/2, then what is cot⁡θ\cot\theta equal to?

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  4. Question 4

    This type asked 6 times: CDS 2 2016, CDS 1 2020, CDS 1 2022, CDS 2 2022, CDS 1 2024, CDS 2 2024. This one: CDS 2 2024 See all 6 of this type

    39
    What is (cos⁡θ−sin⁡θ+1cos⁡θ+sin⁡θ−1)(cot⁡θ−cosec θ)\left(\dfrac{\cos\theta - \sin\theta + 1}{\cos\theta + \sin\theta - 1}\right)(\cot\theta - \mathrm{cosec}\,\theta) equal to ?

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  5. Question 5

    This type asked 6 times: CDS 2 2016, CDS 1 2019, CDS 2 2019, CDS 2 2021, CDS 1 2022, CDS 1 2023. This one: CDS 1 2023 See all 6 of this type

    51
    What is the value of cos⁡232∘+cos⁡258∘sec⁡250∘−cot⁡240∘+4tan⁡13∘tan⁡37∘tan⁡53∘tan⁡77∘\frac{\cos^2 32^\circ + \cos^2 58^\circ}{\sec^2 50^\circ - \cot^2 40^\circ} + 4\tan 13^\circ \tan 37^\circ \tan 53^\circ \tan 77^\circ ?

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  6. Question 6

    This type asked 5 times: CDS 1 2020, CDS 2 2023, CDS 1 2024, CDS 1 2025, CDS 2 2026. This one: CDS 2 2026 See all 5 of this type

    36
    If tan⁡6θ⋅tan⁡3θ=1\tan 6\theta \cdot \tan 3\theta = 1, where 0<θ<30∘0 < \theta < 30^\circ, then what is θ\theta equal to ?

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  7. Question 7

    This type asked 5 times: CDS 2 2016, CDS 1 2018, CDS 2 2018, CDS 1 2019, CDS 2 2026. This one: CDS 2 2026 See all 5 of this type

    38
    If cos⁡2x+cos⁡4x=1\cos^2 x + \cos^4 x = 1, where 0<x<π20 < x < \frac{\pi}{2}, then what is (sin⁡2x+sin⁡3x)+(sin⁡3x+sin⁡4x)(\sin^2 x + \sin^3 x) + (\sin^3 x + \sin^4 x) equal to ?

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  8. Question 8

    This type asked 5 times: CDS 2 2020, CDS 1 2021, CDS 1 2023, CDS 1 2024, CDS 2 2026. This one: CDS 2 2026 See all 5 of this type

    47
    What is the ratio of the greatest value of sin⁡2x+2\sin^2 x + 2 (where 0≤x≤π20 \le x \le \frac{\pi}{2}) to its least value ?

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  9. Question 9

    This type asked 5 times: CDS 2 2018, CDS 2 2020, CDS 1 2021, CDS 2 2024, CDS 1 2025. This one: CDS 1 2025 See all 5 of this type

    24
    Consider the following statements : I. (cosec⁡α−sec⁡α)(\operatorname{cosec} \alpha - \sec \alpha) is always positive in the first quadrant. II. (tan⁡α−cot⁡α)(\tan \alpha - \cot \alpha) is always negative in the first quadrant. Which of the statements given above is/are correct ?

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  10. Question 10

    This type asked 5 times: CDS 2 2018, CDS 2 2020, CDS 1 2021, CDS 2 2023, CDS 1 2025. This one: CDS 1 2025 See all 5 of this type

    29
    Which of the following equations is/are possible ? I. sin⁡2θ=(x+y)24xy\sin^2\theta = \frac{(x+y)^2}{4xy}, where x, y are positive unequal real quantities. II. sin⁡θ+cos⁡θ=x+1x\sin\theta + \cos\theta = x + \frac{1}{x}, where x is a positive real quantity. Select the correct answer using the code given below :

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