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Saturday, 31 October

JEE Main · Maths · Continuity and Differentiability

Periodic Reduction of tan-1(tan x) and cot-1(cot x)

JEE Main asked Periodic Reduction of tan-1(tan x) and cot-1(cot x) 2 times in 2 of the 108 shifts Lumi analysed, in 2020 and 2021. It belongs to Inverse Trig Identities, in Continuity and Differentiability (Maths). The longest wait between two years asking it was 1 year.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
2 of 8
First asked
2020
last in 2021
Pattern
Gone quiet
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020 and 2021. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170.08’200.03’210’220’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 1 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 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
  • 20240 of 18
  • 20230 of 12
  • 20220 of 24
  • 20211 of 24
  • 20201 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.

  • Derivative of simplified inverse trig
  • Integrate derivative defined by inverse trig of sec plus tan

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. 27 Aug 2021, Shift 2 · Q67If…MediumSingle correct
  2. 9 Jan 2020, Shift 1 · Q61If f′(x)=tan⁡−1(sec⁡x+tan⁡x)f'(x)=\tan^{-1}(\sec x+\tan x), −π2<x<π2-\frac{\pi}{2}<x<\frac{\pi}{2}, and f(0)=0f(0)=0, then f(1)f(1) is equal to :HardSingle correct

Shifts: 9 Jan 2020, Shift 1, 27 Aug 2021, 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