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Trigonometric Equations

JEE Mains Maths. Try each one first, then open its answer.

Top 10 JEE Mains 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 7 times: 2021 Paper 25, 14 Jun 2022, 25 Jun 2022, 29 Jun 2022, 2 Apr 2025, 3 Apr 2025, 23 Jan 2026 S1. This one: 23 Jan 2026 S1 See all 7 of this type

    66
    Number of solutions of 3cos⁡2θ+8cos⁡θ+33=0,θ∈[−3π,2π]\sqrt{3}\cos2\theta + 8\cos\theta + 3\sqrt{3}= 0,\theta \in \lbrack - 3\pi,2\pi\rbrack is:

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  2. Question 2

    This type asked 4 times: 2021 Paper 14, 25 Jan 2023, 7 Apr 2025, 5 Apr 2026 S2. This one: 5 Apr 2026 S2 See all 4 of this type

    73
    If S={θ∈[−π,π]:cos⁡θcos⁡5θ2=cos⁡7θcos⁡7θ2}S = \left\{ \theta \in \lbrack - \pi,\pi\rbrack:\cos\theta \cos\frac{5\theta}{2} = \cos7\theta\cos\frac{7\theta}{2} \right\}, then n(S)n(S) is equal to .........

  3. Question 3

    This type asked 4 times: 2021 Paper 25, 29 Jan 2023, 27 Jan 2024, 5 Apr 2026 S1. This one: 5 Apr 2026 S1 See all 4 of this type

    62
    The sum of all the integral values of p such that the equation 3sin⁡2x+12cos⁡x−3=p,x∈R3\sin^{2}x+ 12\cos x- 3 =p,x\in R, has at least one solution, is :

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  4. Question 4

    This type asked 4 times: 2021 Paper 5, 2021 Paper 23, 26 Jul 2022, 10 Apr 2023. This one: 10 Apr 2023 See all 4 of this type

    165
    Let S={x∈(−π2,π2):91−tan⁡2x+9tan⁡2x=10}S =\left\{ x \in\left( -\frac{\pi}{2},\frac{\pi}{2} \right):9^{1 -\tan^{2}x}+9^{\tan^{2}x}= 10 \right\} and β=∑x∈Stan⁡2(x3)\beta =\sum_{x \in S} \tan^{2}\left( \frac{x}{3} \right), then 16(β−14)2\frac{1}{6}(\beta - 14)^{2} is equal to

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  5. Question 5

    This type asked 3 times: 29 Jan 2024, 5 Apr 2024, 6 Apr 2026 S1. This one: 6 Apr 2026 S1 See all 3 of this type

    64
    Let S={θ∈(−2π,2π):cos⁡θ+1=3sin⁡θ}S = \{\theta\in ( - 2\pi,2\pi):\cos\theta+ 1 =\sqrt{3}\sin\theta\}. Then ∑θ∈Sθ\sum_{\theta\in S} \theta is equal to:

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  6. Question 6

    This type asked 3 times: 29 Jul 2022, 31 Jan 2024, 1 Feb 2024. This one: 1 Feb 2024 See all 3 of this type

    153
    The number of solutions of the equation 4sin⁡2x−44\sin^{2}x - 4 cos⁡3x+9−4cos⁡x=0;x∈[−2π,2π]\cos^{3}x + 9 - 4\cos x = 0;x \in \lbrack - 2\pi,2\pi\rbrack is:

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  7. Question 7

    Asked 2 times: 26 Jul 2022, 22 Jan 2025 See all 2 times it was asked

    143
    The sum of all values of θ∈[0,2π]\theta \in \lbrack 0,2\pi\rbrack satisfying 2sin⁡2θ=cos⁡2θ2\sin^{2}\theta = \cos2\theta and 2cos⁡2θ=3sin⁡θ2\cos^{2}\theta = 3\sin\theta is

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  8. Question 8

    This type asked 2 times: 2021 Paper 8, 3 Apr 2025. This one: 3 Apr 2025 See all 2 of this type

    60
    The number of solutions of the equation 2x+3tan⁡x=π,x∈[−2π,2π]−2x+ 3\tan x=\pi,x\in\left\lbrack - 2\pi,2\pi \right\rbrack- {±π2,±3π2}\left\{ \pm\frac{\pi}{2}, \pm\frac{3\pi}{2} \right\} is.

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  9. Question 9

    This type asked 2 times: 27 Jan 2024, 30 Jan 2024. This one: 30 Jan 2024 See all 2 of this type

    79
    If 2sin⁡3x+sin⁡2xcos⁡x+4sin⁡x−4=02\sin^{3}x+ \sin2x\cos x+ 4\sin x- 4 = 0 has exactly 3 solutions in the interval [0,nπ2],n∈N\left\lbrack 0,\frac{n\pi}{2} \right\rbrack,n \in N, then the roots of the equation x2+nx+(n−3)=0x^{2}+nx+ (n- 3) = 0 belong to :

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  10. Question 10

    This type asked 2 times: 2021 Paper 9, 25 Jul 2022. This one: 25 Jul 2022 See all 2 of this type

    78
    The number of solutions of ∣cos⁡x∣=sin⁡x|\cos x| = \sin x, such that −4π≤x≤4π- 4\pi \leq x \leq 4\pi is:

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