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Saturday, 31 October

JEE Main · Maths · Inverse Trigonometric Functions

Sine Inverse Sum and Difference

JEE Main asked Sine Inverse Sum and Difference 3 times in 3 of the 108 shifts Lumi analysed, in 2020, 2021 and 2023. 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
3
in 3 shifts
Years
3 of 8
First asked
2020
last in 2023
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021 and 2023. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170.08’200.03’210’220.07’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 1 in 24 shifts · 2022: 0 in 24 shifts · 2023: 1 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
  • 20231 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.

  • Count solutions of inverse trig equation
  • Sum of inverse sine terms

Difficulty

Easy 0Medium 2Hard 1

1 of the 3 questions had a numerical answer.

Every question

All 3 questions

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

  1. 13 Apr 2023, Shift 1 · Q30If…HardNumerical value
  2. 16 Mar 2021, Shift 2 · Q78Given that the inverse trigonometric functions take principal values only. Then, the number of real values of xx which satisfy…MediumSingle correct
  3. 3 Sep 2020, Shift 1 · Q692π−(sin⁡−145+sin⁡−1513+sin⁡−11665)2\pi-\left(\sin^{-1}\frac{4}{5}+\sin^{-1}\frac{5}{13}+\sin^{-1}\frac{16}{65}\right) is equal to :MediumSingle correct

Shifts: 3 Sep 2020, Shift 1, 16 Mar 2021, Shift 2, 13 Apr 2023, Shift 1.

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