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Friday, 9 October

JEE Main Maths · Inverse Trigonometric Functions

Inverse Trig Identities in JEE Main

Inverse Trig Identities (Maths, Inverse Trigonometric Functions) came 20 times in 19 of the 42 JEE Main shifts Lumi analysed, across 18 distinct ideas. 13 of them came in 2024–26; it was last asked in 2026.

Questions
20
in 19 shifts
Ideas asked
18
2 asked more than once
Numerical answer
5
25% of its questions
Pattern
Asked most years
last asked 2026
Questions each year
0361’171’201’213’221’234’243’256’26

In the shifts Lumi analysed for each year.

Difficulty and format
Easy 0Medium 11Hard 9

Format

  • Single correct14 Q
  • Numerical value5 Q
  • Two statements1 Q
Ideas inside the topic
18 ideas
Where it sits

Part of Inverse Trigonometric Functions, which had 25 questions in all. Inverse Trig Identities accounts for 80% of them. In Lumi's JEE taxonomy it belongs to Trigonometry.

Some questions sit in other chapters too: Continuity and Differentiability, Integrals.

Every question

All 20 Inverse Trig Identities questions

Newest first, each with its options and official answer.

  1. 4 Apr 2026, Shift 1 · Q16If y=tan⁡−1(3cos⁡x−4sin⁡x4cos⁡x+3sin⁡x)+2tan⁡−1(x1+1−x2)y=\tan^{-1}\left(\frac{3\cos x-4\sin x}{4\cos x+3\sin x}\right)+2\tan^{-1}\left(\frac{x}{1+\sqrt{1-x^2}}\right), then dydx\frac{dy}{dx}…MediumSingle correct
  2. 4 Apr 2026, Shift 2 · Q20The integral ∫01cot⁡−1(1+x+x2)dx\int_0^1\cot^{-1}\left(1+x+x^2\right)dx is equal to:HardSingle correct
  3. 5 Apr 2026, Shift 1 · Q24If π4+∑p=111tan⁡−1(2p−11+22p−1)=α\frac{\pi}{4} + \sum_{p=1}^{11} \tan^{-1}\left(\frac{2^{p-1}}{1 + 2^{2p-1}}\right) = \alpha, then tan⁡α\tan\alpha is equal to ________.MediumNumerical value
  4. 6 Apr 2026, Shift 1 · Q13Let 0<α<10<\alpha<1, β=13α\beta=\frac{1}{3\alpha} and tan⁡−1(1−α)+tan⁡−1(1−β)=π4\tan^{-1}(1-\alpha)+\tan^{-1}(1-\beta)=\frac{\pi}{4}. Then 6(α+β)6(\alpha+\beta) is equal to:MediumSingle correct
  5. 6 Apr 2026, Shift 2 · Q13If sin⁡(tan⁡−1(x2))=cot⁡(sin⁡−11−x2)\sin\left(\tan^{-1}\left(x\sqrt{2}\right)\right)=\cot\left(\sin^{-1}\sqrt{1-x^2}\right), x∈(0,1)x\in(0,1), then the value of xx is :MediumSingle correct
  6. 8 Apr 2026, Shift 2 · Q12Let α=3sin⁡−1(611)\alpha = 3\sin^{-1}\left(\frac{6}{11}\right) and β=3cos⁡−1(49)\beta = 3\cos^{-1}\left(\frac{4}{9}\right), where inverse trigonometric functions…HardTwo statements
  7. 2 Apr 2025, Shift 2 · Q23If y=cos⁡(π3+cos⁡−1x2)y = \cos\left(\frac{\pi}{3} + \cos^{-1}\frac{x}{2}\right), then (x−y)2+3y2(x-y)^2 + 3y^2 is equal to __________.MediumNumerical value
  8. 4 Apr 2025, Shift 2 · Q13The sum of the infinite series…HardSingle correct
  9. 8 Apr 2025, Shift 2 · Q13The value of…HardSingle correct
  10. 9 Apr 2024, Shift 2 · Q11The integral ∫1/43/4cos⁡(2cot⁡−11−x1+x)dx\int_{1/4}^{3/4}\cos\left(2\cot^{-1}\sqrt{\frac{1-x}{1+x}}\right)dx is equal toMediumSingle correct
  11. 9 Apr 2024, Shift 2 · Q30Let the inverse trigonometric functions take principal values. The number of real solutions of the equation…MediumNumerical value
  12. 31 Jan 2024, Shift 1 · Q20For α,β,γ≠0\alpha,\beta,\gamma\neq0, if sin⁡−1α+sin⁡−1β+sin⁡−1γ=π\sin^{-1}\alpha+\sin^{-1}\beta+\sin^{-1}\gamma=\pi and…HardSingle correct
  13. 31 Jan 2024, Shift 2 · Q20If a=sin⁡−1(sin⁡(5))a=\sin^{-1}(\sin(5)) and b=cos⁡−1(cos⁡(5))b=\cos^{-1}(\cos(5)), then a2+b2a^2+b^2 is equal toMediumSingle correct
  14. 13 Apr 2023, Shift 2 · Q30For x∈(−1,1]x\in(-1,1], the number of solutions of the equation sin⁡−1x=2tan⁡−1x\sin^{-1}x=2\tan^{-1}x is equal to ______.HardNumerical value
  15. 28 Jul 2022, Shift 1 · Q4Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation…HardSingle correct
  16. 24 Jun 2022, Shift 1 · Q8The set of all values of k for which (tan⁡−1x)3+(cot⁡−1x)3=kπ3, x∈R(\tan^{-1}x)^3 + (\cot^{-1}x)^3 = k\pi^3,\ x \in \mathbf{R}, is the interval :HardSingle correct
  17. 29 Jun 2022, Shift 1 · Q26…MediumNumerical value
  18. 16 Mar 2021, Shift 2 · Q78Given that the inverse trigonometric functions take principal values only. Then, the number of real values of xx which satisfy…MediumSingle correct
  19. 8 Jan 2020, Shift 1 · Q69Let f(x)=(sin⁡(tan⁡−1x)+sin⁡(cot⁡−1x))2−1f(x)=\left(\sin(\tan^{-1}x)+\sin(\cot^{-1}x)\right)^2-1, ∣x∣>1|x|>1. If…HardSingle correct
  20. 2 Apr 2017 (offline) · Q71If for x∈(0,14)x\in\left(0,\frac{1}{4}\right), the derivative of tan⁡−1(6xx1−9x3)\tan^{-1}\left(\frac{6x\sqrt{x}}{1-9x^3}\right) is x⋅g(x)\sqrt{x}\cdot g(x), then…MediumSingle correct