JEE Main · Maths · Inverse Trigonometric Functions
Inverse Trig Identities: JEE Main previous year questions
51 questions in the 108 JEE Main shifts Lumi analysed, in 8 of 8 years. Pattern: Asked most years. 16 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 51
- in 48 of 108 shifts
- Years asked
- 8/8
- last asked 2026
- Weighted estimate
- 0.5
- model; history: 0.5 a shift on average, typically 0.3–0.7
Key findings
- 01
Asked in 8 of 8 years with analysed shifts and in 48 of 108 shifts: 51 questions, #54 of 196 topics. It came in every year with analysed shifts.
- 02
54% of its questions since 2020 tested an idea no earlier year had asked; 10 repeated an idea from the year before.
- 03
The most repeated idea is Complementary Identities, asked 7 times in 7 shifts (2021, 2022, 2024), most often as “count solutions of inverse trig equation”.
- 04
JEE Main has asked 25 of the 65 ideas in this topic; 36 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (76%); 22% need a numerical answer, 4% are easy and 31% hard.
- 06
The skill tested most is multi-step (78%), then calculation (16%).
Questions a shift, year by year
Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.
Raw count: 2017: 1 in 1 shift · 2020: 4 in 12 shifts · 2021: 12 in 24 shifts · 2022: 16 in 24 shifts · 2023: 2 in 12 shifts · 2024: 7 in 18 shifts · 2025: 3 in 8 shifts · 2026: 6 in 9 shifts.
- Up to 2023
- 0.5
- a shift, of 25
- Since 2024
- 0.5
- 0.0
- Usual gap
- 1.3 yrs
- between years asking it
- Shifts with it
- 48/108
- 44% of analysed shifts
How it is asked
Difficulty, format and skill
Across all 51 questions on Inverse Trig Identities since 2017.
Difficulty
QUESTIONS- Easy2 · 4%
- Medium33 · 65%
- Hard16 · 31%
Format
SHARE- Single correct · 39 Q76%
- Numerical value · 11 Q22%
- Two statements · 1 Q2%
Skill tested
SHARE- Multi-step · 40 Q78%
- Calculation · 8 Q16%
- Application · 3 Q6%
Repeats
New idea, or one asked before?
Each column is a year. Blue questions tested an idea no earlier year had asked; navy ones went back to an idea from an earlier year. 2017 is the first year, so everything in it counts as new. Heights are question counts, and Lumi analysed 1 to 24 shifts a year, so compare the split inside a column rather than heights across years.
- Idea asked for the first time
- Idea asked in an earlier year
Coverage of the topic
JEE Main has asked 25 of the 65 ideas in this topic. 36 have never been asked yet.
- Asked directly25 · 38%
- Touched inside another question4 · 6%
- Never asked36 · 55%
Ideas come from Lumi’s JEE syllabus map. A never-asked idea is not a safe skip: across all of JEE Main, 22% of questions since 2024 tested an idea no earlier year had asked.
Drill down
Chapter, idea, question
Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.
22 ideas inside
Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.
Ideas
Every idea inside this topic
25 different ideas were tested; 12 came more than once.
count solutions of inverse trig equation
Single correct · 7 shifts · 1 numericalsum of telescoping inverse trig series
Single correct · 5 shifts · 2 numericaltan inverse sum equation with constraint
Single correct · 4 shiftsexpression from trig of inverse trig sum
Numerical value · 4 shifts · 2 numericalsolve equation with trig of inverse trig
Single correct · 3 shifts · 1 numericalcount solutions of inverse trig equation
Single correct · 3 shifts · 1 numericaldefinite integral of inverse trig function
Numerical value · 2 shifts · 1 numericalevaluate inverse trig expression with branch trap
Single correct · 2 shiftssum of infinite cot inverse series
Single correct · 2 shiftsdefinite integral after inverse trig simplification
Single correct · 2 shiftsprincipal values of sin-1(sin x) and cos-1(cos x)
Single correct · 2 shiftsderivative of simplified inverse trig
Single correct · 2 shiftsstatement i/ii on inverse trig values
Two statements · 1 shiftdifferentiate simplified inverse trig expression
Single correct · 1 shiftconditional identity on sum of inverse sines
Single correct · 1 shiftcount solutions of inverse trig equation
Numerical value · 1 shift · 1 numericalsum over solutions of inverse trig equation
Numerical value · 1 shift · 1 numericalsum of solutions of inverse trig equation
Single correct · 1 shiftsum of solutions of inverse trig equation
Numerical value · 1 shift · 1 numericalrange of combined inverse trig function
Single correct · 1 shiftevaluate tan of sum of inverse trig terms
Single correct · 1 shiftsum of telescoping inverse trig series
Single correct · 1 shiftevaluate tan of fraction of inverse sine
Single correct · 1 shiftpiecewise branch of inverse trig composite
Single correct · 1 shiftderivative of simplified inverse tan expression
Single correct · 1 shift
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Complementary Identitiescount solutions of inverse trig equation | 7 | 7 | Single correctMulti-step | 1 | |
| Telescoping Inverse Trig Seriessum of telescoping inverse trig series | 5 | 5 | Single correctMulti-step | 2 | |
| Tan-1 Sum and Differencetan inverse sum equation with constraint | 4 | 4 | Single correctMulti-step | – | |
| Trig of Sum of Inverse Trig Functionsexpression from trig of inverse trig sum | 4 | 4 | Numerical valueCalculation | 2 | |
| Evaluating Trig of Inverse Trigsolve equation with trig of inverse trig | 3 | 3 | Single correctApplication | 1 | |
| Sine Inverse Sum and Differencecount solutions of inverse trig equation | 3 | 3 | Single correctMulti-step | 1 | |
| Piecewise cot-1 to tan-1 Conversiondefinite integral of inverse trig function | 2 | 2 | Numerical valueCalculation | 1 | |
| Inverse Trig Simplification via tan(θ)evaluate inverse trig expression with branch trap | 2 | 2 | Single correctMulti-step | – | |
| Telescoping Series with cot-1sum of infinite cot inverse series | 2 | 2 | Single correctMulti-step | – | |
| Multiple Angle Inverse IDdefinite integral after inverse trig simplification | 2 | 2 | Single correctMulti-step | – | |
| Periodic Reduction of sin-1(sin x) and cos-1(cos x)principal values of sin-1(sin x) and cos-1(cos x) | 2 | 2 | Single correctCalculation | – | |
| Periodic Reduction of tan-1(tan x) and cot-1(cot x)derivative of simplified inverse trig | 2 | 2 | Single correctMulti-step | – | |
| Compound Trigonometric Ratios of Inverse Sumsstatement i/ii on inverse trig values | 1 | 1 | Two statementsMulti-step | – | |
| Simplifying tan-1 with a cos x and b sin xdifferentiate simplified inverse trig expression | 1 | 1 | Single correctMulti-step | – | |
| Conditional Identity: Sum of sin-1 to piconditional identity on sum of inverse sines | 1 | 1 | Single correctMulti-step | – | |
| Graphical Root Counting for Mixed Equationscount solutions of inverse trig equation | 1 | 1 | Numerical valueMulti-step | 1 | |
| 2tan-1(x) to sin-1 and cos-1 Conversionssum over solutions of inverse trig equation | 1 | 1 | Numerical valueMulti-step | 1 | |
| Cosine Inverse Sum and Differencesum of solutions of inverse trig equation | 1 | 1 | Single correctMulti-step | – | |
| Extreme Value Principle in Equationssum of solutions of inverse trig equation | 1 | 1 | Numerical valueMulti-step | 1 | |
| Range of Combined Inverse Trig Functionsrange of combined inverse trig function | 1 | 1 | Single correctMulti-step | – | |
| Sum of Three Inverse Tangentsevaluate tan of sum of inverse trig terms | 1 | 1 | Single correctCalculation | – | |
| Telescoping cot^-1 Quadratic Tricksum of telescoping inverse trig series | 1 | 1 | Single correctMulti-step | – | |
| Half-Angle Inverse Trig Evaluationsevaluate tan of fraction of inverse sine | 1 | 1 | Single correctMulti-step | – | |
| sin^-1(2x/(1+x^2)) Piecewise Conversionpiecewise branch of inverse trig composite | 1 | 1 | Single correctMulti-step | – | |
| tan^-1(2x/(1-x^2)) Piecewise Conversionderivative of simplified inverse tan expression | 1 | 1 | Single correctMulti-step | – |
Times and shifts count every analysed shift. Across JEE Main, 78% of questions since 2024 went back to an idea an earlier year had asked; the rest were new. All repeated ideas
Every question
Inverse Trig Identities questions, year by year
The newest 40 show their opening words as they appeared in the official paper; older ones name the idea they tested. Open one for its options and the official answer.
JEE Main 20266 questions in 6 shifts
- 4 Apr, Shift 1Q16If , then …
Idea: Simplifying tan-1 with a cos x and b sin x
New ideaMediumSingle correct - 4 Apr, Shift 2Q20The integral is equal to:
Idea: Piecewise cot-1 to tan-1 Conversion
HardSingle correct - 5 Apr, Shift 1Q24If , then is equal to ________.
Idea: Telescoping Inverse Trig Series
MediumNumerical value - 6 Apr, Shift 1Q13Let , and . Then is equal to:
Idea: Tan-1 Sum and Difference
MediumSingle correct - 6 Apr, Shift 2Q13If , , then the value of is :
Idea: Evaluating Trig of Inverse Trig
MediumSingle correct - 8 Apr, Shift 2Q12Let and , where inverse trigonometric functions…
Idea: Compound Trigonometric Ratios of Inverse Sums
New ideaHardTwo statements
JEE Main 20253 questions in 3 shifts
- 2 Apr, Shift 2Q23If , then is equal to __________.
Idea: Trig of Sum of Inverse Trig Functions
MediumNumerical value - 4 Apr, Shift 2Q13The sum of the infinite series…
Idea: Telescoping Series with cot-1
HardSingle correct - 8 Apr, Shift 2Q13The value of…
Idea: Inverse Trig Simplification via tan(θ)
HardSingle correct
JEE Main 20247 questions in 6 shifts
- 4 Apr, Shift 2Q20Given that the inverse trigonometric function assumes principal values only. Let , be any two real numbers in such that…
Idea: Complementary Identities
HardSingle correct - 6 Apr, Shift 1Q30For , if , then is equal to __________.
Idea: Piecewise cot-1 to tan-1 Conversion
New ideaMediumNumerical value - 9 Apr, Shift 2Q11The integral is equal to
Idea: Multiple Angle Inverse ID
MediumSingle correct - 9 Apr, Shift 2Q30Let the inverse trigonometric functions take principal values. The number of real solutions of the equation…
Idea: Complementary Identities
MediumNumerical value - 1 Feb, Shift 1Q20If , and ,…
Idea: Tan-1 Sum and Difference
MediumSingle correct - 31 Jan, Shift 1Q20For , if and…
Idea: Conditional Identity: Sum of sin-1 to pi
New ideaHardSingle correct - 31 Jan, Shift 2Q20If and , then is equal to
Idea: Periodic Reduction of sin-1(sin x) and cos-1(cos x)
MediumSingle correct
JEE Main 20232 questions in 2 shifts
- 13 Apr, Shift 1Q30If…
Idea: Sine Inverse Sum and Difference
HardNumerical value - 13 Apr, Shift 2Q30For , the number of solutions of the equation is equal to ______.
Idea: Graphical Root Counting for Mixed Equations
New ideaHardNumerical value
JEE Main 202216 questions in 15 shifts
- 25 Jul, Shift 2Q30Let and . If…
Idea: 2tan-1(x) to sin-1 and cos-1 Conversions
New ideaMediumNumerical value - 26 Jul, Shift 1Q19is equal to :
Idea: Sum of Three Inverse Tangents
New ideaMediumSingle correct - 26 Jul, Shift 2Q16If and , then a value of…
Idea: Complementary Identities
Asked the year beforeMediumSingle correct - 27 Jul, Shift 1Q21For , let the solutions of the equation…
Idea: Evaluating Trig of Inverse Trig
New ideaHardNumerical value - 28 Jul, Shift 1Q4Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation…
Idea: Cosine Inverse Sum and Difference
New ideaHardSingle correct - 30 Jul, Shift 2Q90Let…
Idea: Extreme Value Principle in Equations
New ideaHardNumerical value - 24 Jun, Shift 1Q8The set of all values of k for which , is the interval :
Idea: Complementary Identities
Asked the year beforeHardSingle correct - 24 Jun, Shift 2Q1Let and . Then a value of is
Idea: Inverse Trig Simplification via tan(θ)
New ideaMediumSingle correct - 25 Jun, Shift 2Q19The value of is equal to :
Idea: Periodic Reduction of sin-1(sin x) and cos-1(cos x)
New ideaEasySingle correct - 26 Jun, Shift 1Q19Let , . If is the range of the function , then is…
Idea: Range of Combined Inverse Trig Functions
New ideaMediumSingle correct - 26 Jun, Shift 2Q19If the inverse trigonometric functions take principal values, then…
Idea: Evaluating Trig of Inverse Trig
New ideaEasySingle correct - 27 Jun, Shift 2Q18The value of is
Idea: Telescoping cot^-1 Quadratic Trick
New ideaMediumSingle correct - 28 Jun, Shift 2Q18The value of is equal to :
Idea: Telescoping Inverse Trig Series
Asked the year beforeMediumSingle correct - 29 Jun, Shift 1Q26…
Idea: Trig of Sum of Inverse Trig Functions
Asked the year beforeMediumNumerical value - 30 Jun, Shift 1Q10Let m and M respectively be the minimum and the maximum values of ,…
Idea: Complementary Identities
Asked the year beforeMediumSingle correct - 30 Jun, Shift 1Q19Let and…
Idea: Trig of Sum of Inverse Trig Functions
Asked the year beforeMediumSingle correct
JEE Main 202112 questions in 11 shifts
- 26 Aug, Shift 1Q68Let , . Then :
Idea: Multiple Angle Inverse ID
New ideaHardSingle correct - 26 Aug, Shift 2Q77If , then the value of is :
Idea: Telescoping Inverse Trig Series
Asked the year beforeMediumSingle correct - 27 Aug, Shift 1Q76If ; , , then the value of is :
Idea: Complementary Identities
New ideaMediumSingle correct - 27 Aug, Shift 2Q67If…
Idea: Periodic Reduction of tan-1(tan x) and cot-1(cot x)
Asked the year beforeMediumSingle correct - 24 Feb, Shift 1Q90is equal to ___________.
Idea: Telescoping Inverse Trig Series
Asked the year beforeMediumNumerical value - 24 Feb, Shift 2Q74A possible value of is :
Idea: Half-Angle Inverse Trig Evaluations
New ideaMediumSingle correct - 25 Feb, Shift 2 · Q79Trig of Sum of Inverse Trig FunctionsNew ideaMedium
- 26 Feb, Shift 1 · Q76Complementary IdentitiesNew ideaMedium
- 26 Feb, Shift 2 · Q64Tan-1 Sum and DifferenceNew ideaMedium
- 16 Mar, Shift 2 · Q78Sine Inverse Sum and DifferenceAsked the year beforeMedium
- 17 Mar, Shift 1 · Q68Telescoping Series with cot-1New ideaMedium
- 17 Mar, Shift 1 · Q80Tan-1 Sum and DifferenceNew ideaHard
JEE Main 20204 questions in 4 shifts
JEE Main 20171 question in 1 shift
Questions from the official JEE Main Paper 1 shifts published by NTA (CBSE for 2017). Questions NTA dropped are left out. Topic and idea tags, counts and notes are Lumi’s.