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Friday, 9 October

JEE Main Maths · Trigonometric Functions

Trigonometric Identities in JEE Main

Trigonometric Identities (Maths, Trigonometric Functions) came 14 times in 14 of the 42 JEE Main shifts Lumi analysed, across 12 distinct ideas. 10 of them came in 2024–26; it was last asked in 2026.

Questions
14
in 14 shifts
Ideas asked
12
2 asked more than once
Numerical answer
2
14% of its questions
Pattern
Asked most years
last asked 2026
Questions each year
0361’170’202’210’221’233’242’255’26

In the shifts Lumi analysed for each year.

Difficulty and format
Easy 0Medium 10Hard 4

Format

  • Single correct12 Q
  • Numerical value2 Q
Ideas inside the topic
12 ideas
Where it sits

Part of Trigonometric Functions, which had 41 questions in all. Trigonometric Identities accounts for 34% of them. In Lumi's JEE taxonomy it belongs to Trigonometry.

Some questions sit in other chapters too: Complex Numbers and Quadratic Equations, Determinants, Integrals, Sequences and Series.

Every question

All 14 Trigonometric Identities questions

Newest first, each with its options and official answer.

  1. 2 Apr 2026, Shift 1 · Q11If sin⁡(π18)sin⁡(5π18)sin⁡(7π18)=K\sin\left(\frac{\pi}{18}\right)\sin\left(\frac{5\pi}{18}\right)\sin\left(\frac{7\pi}{18}\right)=K, then the value of…MediumSingle correct
  2. 2 Apr 2026, Shift 2 · Q13Let P={θ∈[0,4π]:tan⁡2θ≠1}P = \{\theta \in [0, 4\pi]: \tan^2\theta \ne 1\} and…MediumSingle correct
  3. 4 Apr 2026, Shift 1 · Q23If A=sin⁡3∘cos⁡9∘+sin⁡9∘cos⁡27∘+sin⁡27∘cos⁡81∘A=\frac{\sin 3^\circ}{\cos 9^\circ}+\frac{\sin 9^\circ}{\cos 27^\circ}+\frac{\sin 27^\circ}{\cos 81^\circ} and…MediumNumerical value
  4. 5 Apr 2026, Shift 1 · Q6Let tan⁡A\tan A, tan⁡B\tan B, where A,B∈(−π2,π2)A, B \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right), be the roots of the quadratic equation…MediumSingle correct
  5. 8 Apr 2026, Shift 2 · Q22If…HardNumerical value
  6. 4 Apr 2025, Shift 2 · Q3Let the product of ω1=(8+i)sin⁡θ+(7+4i)cos⁡θ\omega_1=(8+i)\sin\theta+(7+4i)\cos\theta and ω2=(1+8i)sin⁡θ+(4+7i)cos⁡θ\omega_2=(1+8i)\sin\theta+(4+7i)\cos\theta be α+iβ\alpha+i\beta,…HardSingle correct
  7. 7 Apr 2025, Shift 1 · Q1If for θ∈[−π3,0]\theta \in \left[-\frac{\pi}{3}, 0\right], the points…MediumSingle correct
  8. 9 Apr 2024, Shift 1 · Q20Let ∣cos⁡θcos⁡(60∘−θ)cos⁡(60∘+θ)∣≤18\left|\cos\theta\cos(60^\circ-\theta)\cos(60^\circ+\theta)\right|\le\frac{1}{8}, θ∈[0,2π]\theta\in[0,2\pi]. Then, the sum of all…MediumSingle correct
  9. 9 Apr 2024, Shift 2 · Q1Let the range of the function f(x)=12+sin⁡3x+cos⁡3x, x∈Rf(x)=\frac{1}{2+\sin 3x+\cos 3x},\ x\in\mathbb{R} be [a,b][a, b]. If α\alpha and β\beta are respectively…MediumSingle correct
  10. 30 Jan 2024, Shift 2 · Q11For α,β∈(0,π/2)\alpha, \beta \in (0, \pi/2), let 3sin⁡(α+β)=2sin⁡(α−β)3\sin(\alpha + \beta) = 2\sin(\alpha - \beta) and a real number kk be such that…MediumSingle correct
  11. 8 Apr 2023, Shift 2 · Q19The value of 36(4cos⁡29∘−1)(4cos⁡227∘−1)(4cos⁡281∘−1)(4cos⁡2243∘−1)36(4\cos^2 9^\circ - 1)(4\cos^2 27^\circ - 1)(4\cos^2 81^\circ - 1)(4\cos^2 243^\circ - 1) isHardSingle correct
  12. 3 Aug 2021, Shift 2 · Q79The maximum value of (cos⁡θ1)⋅(cos⁡θ2)⋅(cos⁡θ3)⋅…⋅(cos⁡θ10)(\cos\theta_1)\cdot(\cos\theta_2)\cdot(\cos\theta_3)\cdot\ldots\cdot(\cos\theta_{10}) under the restrictions…HardSingle correct
  13. 16 Mar 2021, Shift 2 · Q77The maximum value of…MediumSingle correct
  14. 2 Apr 2017 (offline) · Q88If 5(tan⁡2x−cos⁡2x)=2cos⁡2x+95(\tan^2x-\cos^2x)=2\cos2x+9, then the value of cos⁡4x\cos4x is :MediumSingle correct