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Saturday, 31 October

JEE Main · Maths · Integrals

Multiple Angle Inverse ID

JEE Main asked Multiple Angle Inverse ID 2 times in 2 of the 108 shifts Lumi analysed, in 2021 and 2024. It belongs to Inverse Trig Identities, in Integrals (Maths). The longest wait between two years asking it was 3 years.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
2 of 8
First asked
2021
last in 2024
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

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

00.050.10’170’200.03’210’220’230.05’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 1 in 18 shifts · 2025: 0 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
  • 20250 of 8
  • 20241 of 18
  • 20230 of 12
  • 20220 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

Single correct is the usual form. Skill tested: multi-step.

  • Definite integral after inverse trig simplification
  • Simplify nested inverse trig function

Difficulty

Easy 0Medium 1Hard 1

Every question was multiple choice.

Every question

All 2 questions

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

  1. 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
  2. 26 Aug 2021, Shift 1 · Q68Let f(x)=cos⁡(2tan⁡−1sin⁡(cot⁡−11−xx))f(x) = \cos\left(2\tan^{-1}\sin\left(\cot^{-1}\sqrt{\frac{1-x}{x}}\right)\right), 0<x<10 < x < 1. Then :HardSingle correct

Shifts: 26 Aug 2021, Shift 1, 9 Apr 2024, 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