Learn

Saturday, 31 October

JEE Main · Maths · Trigonometric Functions

Quadratic Substitution in Trigonometry

JEE Main asked Quadratic Substitution in Trigonometry 12 times in 12 of the 108 shifts Lumi analysed, in 2021, 2022, 2023, 2024 and 2025. It belongs to General Solutions, in Trigonometric Functions (Maths). The longest wait between two years asking it was 1 year. In 2021, 2022, 2023, 2024 and 2025 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
12
in 12 shifts
Years
5 of 8
First asked
2021
last in 2025
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022, 2023, 2024 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.20.40’170’200.07’210.11’220.14’230.09’240.38’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 2 in 24 shifts · 2022: 3 in 24 shifts · 2023: 2 in 12 shifts · 2024: 2 in 18 shifts · 2025: 3 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20260 of 9
  • 20253 of 8
  • 20242 of 18
  • 20232 of 12
  • 20223 of 24
  • 20212 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: multi-step.

  • Count solutions of trig equation in interval
  • Count solutions of trigonometric equation in interval

Difficulty

Easy 1Medium 8Hard 3

3 of the 12 questions had a numerical answer.

Every question

All 12 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 3 Apr 2025, Shift 2 · Q13The number of solutions of the equation…HardSingle correct
  2. 2 Apr 2025, Shift 2 · Q13If θ∈[−7π6,4π3]\theta \in \left[-\frac{7\pi}{6}, \frac{4\pi}{3}\right], then the number of solutions of…MediumSingle correct
  3. 2 Apr 2025, Shift 1 · Q3If θ∈[−2π,2π]\theta\in[-2\pi, 2\pi], then the number of solutions of 22cos⁡2θ+(2−6)cos⁡θ−3=02\sqrt{2}\cos^2\theta+(2-\sqrt{6})\cos\theta-\sqrt{3}=0, is equal to :MediumSingle correct
  4. 31 Jan 2024, Shift 2 · Q2The number of solutions, of the equation esin⁡x−2e−sin⁡x=2e^{\sin x}-2e^{-\sin x}=2, is :MediumSingle correct
  5. 1 Feb 2024, Shift 2 · Q20The number of solutions of the equation 4sin⁡2x−4cos⁡3x+9−4cos⁡x=04\sin^2x-4\cos^3x+9-4\cos x=0; x∈[−2π,2π]x\in[-2\pi,2\pi] is :HardSingle correct
  6. 11 Apr 2023, Shift 1 · Q16The number of elements in the set S={θ∈[0,2π]:3cos⁡4θ−5cos⁡2θ−2sin⁡6θ+2=0}S = \{\theta \in [0, 2\pi] : 3\cos^4\theta - 5\cos^2\theta - 2\sin^6\theta + 2 = 0\} isMediumSingle correct
  7. 10 Apr 2023, Shift 2 · Q2Let 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…MediumSingle correct
  8. 29 Jun 2022, Shift 2 · Q24The number of solutions of the equation sin⁡x=cos⁡2x\sin x = \cos^2 x in the interval (0,10)(0, 10) is ___.MediumNumerical value
  9. 29 Jun 2022, Shift 1 · Q24The number of elements in the set S={θ∈[−4π,4π]:3cos⁡22θ+6cos⁡2θ−10cos⁡2θ+5=0}S = \{\theta \in [-4\pi, 4\pi] : 3\cos^2 2\theta + 6\cos 2\theta - 10\cos^2\theta + 5 = 0\} is…MediumNumerical value
  10. 26 Jul 2022, Shift 1 · Q18Let S={θ∈[0, 2π]:82sin⁡2θ+82cos⁡2θ=16}\mathrm{S} = \{\theta \in [0,\ 2\pi] : 8^{2\sin^2\theta} + 8^{2\cos^2\theta} = 16\}. Then…HardSingle correct
  11. 26 Feb 2021, Shift 1 · Q89If 3(cos⁡2x)=(3−1)cos⁡x+1\sqrt{3}(\cos^2 x)=(\sqrt{3}-1)\cos x+1, the number of solutions of the given equation when x∈[0,π2]x\in\left[0,\frac{\pi}{2}\right] is…EasyNumerical value
  12. 31 Aug 2021, Shift 2 · Q78The number of solutions of the equation 32tan⁡2x+32sec⁡2x=8132^{\tan^2 x}+32^{\sec^2 x} = 81, 0≤x≤π40 \le x \le \frac{\pi}{4} is :MediumSingle correct

Shifts: 26 Feb 2021, Shift 1, 31 Aug 2021, Shift 2, 29 Jun 2022, Shift 2, 29 Jun 2022, Shift 1, 26 Jul 2022, Shift 1, 10 Apr 2023, Shift 2, 11 Apr 2023, Shift 1, 31 Jan 2024, Shift 2, 1 Feb 2024, Shift 2, 2 Apr 2025, Shift 2, 2 Apr 2025, Shift 1, 3 Apr 2025, Shift 2.

Same topic

Other ideas in General Solutions

General Solutions has 23 ideas JEE Main has asked; 6 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas