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Saturday, 31 October

JEE Main · Maths · Inverse Trigonometric Functions

Periodic Reduction of sin-1(sin x) and cos-1(cos x)

JEE Main asked Periodic Reduction of sin-1(sin x) and cos-1(cos x) 2 times in 2 of the 108 shifts Lumi analysed, in 2022 and 2024. It belongs to Inverse Trig Identities, in Inverse Trigonometric Functions (Maths). The longest wait between two years asking it was 2 years.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
2 of 8
First asked
2022
last in 2024
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2022 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170’200’210.04’220’230.05’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 1 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
  • 20221 of 24
  • 20210 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: calculation.

  • Principal values of sin-1(sin x) and cos-1(cos x)
  • Simplify inverse trig of trig value

Difficulty

Easy 1Medium 1Hard 0

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. 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
  2. 25 Jun 2022, Shift 2 · Q19The value of tan⁡−1(cos⁡(15π4)−1sin⁡(π4))\tan^{-1}\left(\frac{\cos\left(\frac{15\pi}{4}\right) - 1}{\sin\left(\frac{\pi}{4}\right)}\right) is equal to :EasySingle correct

Shifts: 25 Jun 2022, Shift 2, 31 Jan 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