Learn

Saturday, 31 October

JEE Main · Maths · Inverse Trigonometric Functions

Complementary Identities

JEE Main asked Complementary Identities 7 times in 7 of the 108 shifts Lumi analysed, in 2021, 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. In 2021, 2022 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
7
in 7 shifts
Years
3 of 8
First asked
2021
last in 2024
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200.07’210.11’220’230.09’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 2 in 24 shifts · 2022: 3 in 24 shifts · 2023: 0 in 12 shifts · 2024: 2 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
  • 20242 of 18
  • 20230 of 12
  • 20223 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.

  • Count solutions of inverse trig equation
  • Range of parameter for inverse trig expression

Difficulty

Easy 0Medium 5Hard 2

1 of the 7 questions had a numerical answer.

Every question

All 7 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 · Q30Let the inverse trigonometric functions take principal values. The number of real solutions of the equation…MediumNumerical value
  2. 4 Apr 2024, Shift 2 · Q20Given that the inverse trigonometric function assumes principal values only. Let xx, yy be any two real numbers in [−1,1][-1,1] such that…HardSingle correct
  3. 30 Jun 2022, Shift 1 · Q10Let m and M respectively be the minimum and the maximum values of f(x)=sin⁡−12x+sin⁡2x+cos⁡−12x+cos⁡2xf(x) = \sin^{-1}2x + \sin 2x + \cos^{-1}2x + \cos 2x,…MediumSingle correct
  4. 24 Jun 2022, Shift 1 · Q8The set of all values of k for which (tan⁡−1x)3+(cot⁡−1x)3=kπ3, x∈R(\tan^{-1}x)^3 + (\cot^{-1}x)^3 = k\pi^3,\ x \in \mathbf{R}, is the interval :HardSingle correct
  5. 26 Jul 2022, Shift 2 · Q16If 0<x<120<x<\frac{1}{\sqrt{2}} and sin⁡−1xα=cos⁡−1xβ\frac{\sin^{-1}x}{\alpha}=\frac{\cos^{-1}x}{\beta}, then a value of…MediumSingle correct
  6. 26 Feb 2021, Shift 1 · Q76If sin⁡−1xa=cos⁡−1xb=tan⁡−1yc\frac{\sin^{-1}x}{a}=\frac{\cos^{-1}x}{b}=\frac{\tan^{-1}y}{c} ; 0<x<10<x<1, then the value of cos⁡(πca+b)\cos\left(\frac{\pi c}{a+b}\right) is :MediumSingle correct
  7. 27 Aug 2021, Shift 1 · Q76If (sin⁡−1x)2−(cos⁡−1x)2=a(\sin^{-1}x)^2-(\cos^{-1}x)^2=a ; 0<x<10<x<1, a≠0a\neq 0, then the value of 2x2−12x^2-1 is :MediumSingle correct

Shifts: 26 Feb 2021, Shift 1, 27 Aug 2021, Shift 1, 24 Jun 2022, Shift 1, 30 Jun 2022, Shift 1, 26 Jul 2022, Shift 2, 4 Apr 2024, Shift 2, 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