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Saturday, 31 October

JEE Main · Maths · Inverse Trigonometric Functions

Tan-1 Sum and Difference

JEE Main asked Tan-1 Sum and Difference 4 times in 4 of the 108 shifts Lumi analysed, in 2021, 2024 and 2026. It belongs to Inverse Trig Identities, in Inverse Trigonometric Functions (Maths). The longest wait between two years asking it was 3 years. In 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
4
in 4 shifts
Years
3 of 8
First asked
2021
last in 2026
Pattern
Frequent
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170’200.07’210’220’230.05’240’250.11’26

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

Shift by shift

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

  • 20261 of 9
  • 20250 of 8
  • 20241 of 18
  • 20230 of 12
  • 20220 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.

  • Tan inverse sum equation with constraint
  • Sum of inverse tangents identity

Difficulty

Easy 0Medium 3Hard 1

Every question was multiple choice.

Every question

All 4 questions

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

  1. 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
  2. 1 Feb 2024, Shift 1 · Q20If tan⁡A=1x(x2+x+1)\tan A=\frac{1}{\sqrt{x(x^2+x+1)}}, tan⁡B=xx2+x+1\tan B=\frac{\sqrt{x}}{\sqrt{x^2+x+1}} and tan⁡C=(x−3+x−2+x−1)1/2\tan C=\left(x^{-3}+x^{-2}+x^{-1}\right)^{1/2},…MediumSingle correct
  3. 17 Mar 2021, Shift 1 · Q80The sum of possible values of xx for tan⁡−1(x+1)+cot⁡−1(1x−1)=tan⁡−1(831)\tan^{-1}(x+1)+\cot^{-1}\left(\frac{1}{x-1}\right)=\tan^{-1}\left(\frac{8}{31}\right) is :HardSingle correct
  4. 26 Feb 2021, Shift 2 · Q64If 0<a,b<10 < a, b < 1, and tan⁡−1a+tan⁡−1b=π4\tan^{-1}a + \tan^{-1}b = \frac{\pi}{4}, then the value of…MediumSingle correct

Shifts: 26 Feb 2021, Shift 2, 17 Mar 2021, Shift 1, 1 Feb 2024, Shift 1, 6 Apr 2026, Shift 1.

Same topic

Other ideas in Inverse Trig Identities

Inverse Trig Identities has 25 ideas JEE Main has asked; 12 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas