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Friday, 9 October

JEE Main Maths · Trigonometric Functions

Quadratic Substitution in Trigonometry

Quadratic Substitution in Trigonometry (Trigonometric Functions) was asked 6 times in 6 JEE Main shifts, 2022–2025, out of the 42 shifts Lumi analysed. 1 of the 6 had a numerical answer.

Times asked
6
in 6 shifts
Years
2022–2025
Usual format
Single correct
Multi-step
Pattern
Comes in cycles
repeats across shifts

How it is asked

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

Difficulty

Easy 0Medium 5Hard 1

Where it sits

Chapter: Trigonometric Functions. Topic: General Solutions, 17 questions over 11 ideas.

Other repeat ideas in this topic

Every time it came

All 6 questions

Newest first, each with its options and official answer.

  1. 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
  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. 3 Apr 2025, Shift 2 · Q13The number of solutions of the equation…HardSingle 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. 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
  6. 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