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Saturday, 31 October

JEE Main · Maths · Inverse Trigonometric Functions

Trig of Sum of Inverse Trig Functions

JEE Main asked Trig of Sum of Inverse Trig Functions 4 times in 4 of the 108 shifts Lumi analysed, in 2021, 2022 and 2025. It belongs to Inverse Trig Identities, in Inverse Trigonometric Functions (Maths). The longest wait between two years asking it was 3 years. In 2022 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 2025
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170’200.03’210.07’220’230’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 2 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 1 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
  • 20251 of 8
  • 20240 of 18
  • 20230 of 12
  • 20222 of 24
  • 20211 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Numerical value is the usual form. Skill tested: calculation.

  • Expression from trig of inverse trig sum
  • Value of trig of inverse trig sums

Difficulty

Easy 0Medium 4Hard 0

2 of the 4 questions had a numerical answer.

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. 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
  2. 30 Jun 2022, Shift 1 · Q19Let α=tan⁡(5π16sin⁡(2cos⁡−1(15)))\alpha = \tan\left(\frac{5\pi}{16}\sin\left(2\cos^{-1}\left(\frac{1}{\sqrt{5}}\right)\right)\right) and…MediumSingle correct
  3. 29 Jun 2022, Shift 1 · Q26…MediumNumerical value
  4. 25 Feb 2021, Shift 2 · Q79cosec[2cot⁡−1(5)+cos⁡−1(45)]\mathrm{cosec}\left[2\cot^{-1}(5) + \cos^{-1}\left(\frac{4}{5}\right)\right] is equal to :MediumSingle correct

Shifts: 25 Feb 2021, Shift 2, 29 Jun 2022, Shift 1, 30 Jun 2022, Shift 1, 2 Apr 2025, Shift 2.

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