JEE Main · Maths · Trigonometric Functions
Trigonometric Identities: JEE Main previous year questions
36 questions in the 108 JEE Main shifts Lumi analysed, in 8 of 8 years. Pattern: Asked most years. 12 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 36
- in 35 of 108 shifts
- Years asked
- 8/8
- last asked 2026
- Weighted estimate
- 0.3
- model; history: 0.4 a shift on average, typically 0.2–0.6
Key findings
- 01
Asked in 8 of 8 years with analysed shifts and in 35 of 108 shifts: 36 questions, #96 of 196 topics. It came in every year with analysed shifts.
- 02
60% of its questions since 2020 tested an idea no earlier year had asked; 6 repeated an idea from the year before.
- 03
The most repeated idea is Values of Non-Standard Specific Angles, asked 6 times in 6 shifts (2021, 2022, 2024), most often as “product of parameter range and trig value”.
- 04
JEE Main has asked 19 of the 64 ideas in this topic; 39 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (78%); 22% need a numerical answer, 6% are easy and 33% hard.
- 06
The skill tested most is multi-step (64%), then calculation (25%).
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: 2 in 12 shifts · 2021: 10 in 24 shifts · 2022: 8 in 24 shifts · 2023: 3 in 12 shifts · 2024: 5 in 18 shifts · 2025: 2 in 8 shifts · 2026: 5 in 9 shifts.
- Up to 2023
- 0.4
- a shift, of 25
- Since 2024
- 0.3
- 0.0
- Usual gap
- 1.3 yrs
- between years asking it
- Shifts with it
- 35/108
- 32% of analysed shifts
How it is asked
Difficulty, format and skill
Across all 36 questions on Trigonometric Identities since 2017.
Difficulty
QUESTIONS- Easy2 · 6%
- Medium22 · 61%
- Hard12 · 33%
Format
SHARE- Single correct · 28 Q78%
- Numerical value · 8 Q22%
Skill tested
SHARE- Multi-step · 23 Q64%
- Calculation · 9 Q25%
- Application · 4 Q11%
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 19 of the 64 ideas in this topic. 39 have never been asked yet.
- Asked directly19 · 30%
- Touched inside another question6 · 9%
- Never asked39 · 61%
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.
16 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
19 different ideas were tested; 9 came more than once.
product of parameter range and trig value
Single correct · 6 shifts · 1 numericaltrigonometric value from roots of quadratic
Single correct · 5 shifts · 2 numericalevaluate trig value from product of sines
Single correct · 3 shifts · 1 numericalsimplify trigonometric expression to constant
Single correct · 2 shiftsrange of reciprocal trigonometric function
Single correct · 2 shiftsproduct of cosines with doubling angles
Single correct · 2 shiftssimplify trigonometric product to constant
Numerical value · 2 shifts · 1 numericalvalue of product of sines of multiples of pi/8
Single correct · 2 shiftsmaximum of trigonometric product under constraint
Single correct · 2 shiftsdefinite integral using cot identity
Numerical value · 1 shift · 1 numericaltelescoping sum of trig terms
Numerical value · 1 shift · 1 numericaleliminate parameter from tangent expressions
Single correct · 1 shiftmax/min of expression from complex product
Single correct · 1 shiftsum of angles where triple-angle cosine is maximum
Single correct · 1 shiftevaluate sum of tangents of special angles
Numerical value · 1 shift · 1 numericaltelescoping trig series and solution set
Single correct · 1 shiftvalue of sum of cosines of multiples of angle
Single correct · 1 shiftratio of alternating trig series
Single correct · 1 shiftfind cos4x from trig equation
Single correct · 1 shift
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Values of Non-Standard Specific Anglesproduct of parameter range and trig value | 6 | 6 | Single correctCalculation | 1 | |
| Compound Angle Formulastrigonometric value from roots of quadratic | 5 | 5 | Single correctMulti-step | 2 | |
| Sine Product Identity with 60 Degreesevaluate trig value from product of sines | 3 | 3 | Single correctCalculation | 1 | |
| High Power Reduction Identitiessimplify trigonometric expression to constant | 2 | 2 | Single correctMulti-step | – | |
| Extrema of Linear Trigonometric Formsrange of reciprocal trigonometric function | 2 | 2 | Single correctMulti-step | – | |
| Product of Cosines with Doubling Anglesproduct of cosines with doubling angles | 2 | 2 | Single correctCalculation | – | |
| Triple Angle Formulassimplify trigonometric product to constant | 2 | 2 | Numerical valueApplication | 1 | |
| Product to Sum Formulasvalue of product of sines of multiples of pi/8 | 2 | 2 | Single correctCalculation | – | |
| Trigonometric Bounds and Inequalitiesmaximum of trigonometric product under constraint | 2 | 2 | Single correctApplication | – | |
| Tangent and Cotangent Difference Identitiesdefinite integral using cot identity | 1 | 1 | Numerical valueMulti-step | 1 | |
| Tangent Sum/Difference to Sine Ratiotelescoping sum of trig terms | 1 | 1 | Numerical valueMulti-step | 1 | |
| Elimination of Trigonometric Parameterseliminate parameter from tangent expressions | 1 | 1 | Single correctMulti-step | – | |
| Extrema of Quadratic Trigonometric Formsmax/min of expression from complex product | 1 | 1 | Single correctMulti-step | – | |
| Cosine Product Identity with 60 Degreessum of angles where triple-angle cosine is maximum | 1 | 1 | Single correctMulti-step | – | |
| Products of Tangents of Complementary Anglesevaluate sum of tangents of special angles | 1 | 1 | Numerical valueCalculation | 1 | |
| Telescopic Trigonometric Seriestelescoping trig series and solution set | 1 | 1 | Single correctMulti-step | – | |
| Trigonometric Sums via Roots of Unityvalue of sum of cosines of multiples of angle | 1 | 1 | Single correctCalculation | – | |
| Trigonometric Series with Angles in APratio of alternating trig series | 1 | 1 | Single correctMulti-step | – | |
| Multiple Angle Formulasfind cos4x from trig equation | 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
Trigonometric Identities questions, year by year
The opening words of each question as it appeared in the official paper, with the idea it tested. Open one for its options and the official answer.
JEE Main 20265 questions in 5 shifts
- 2 Apr, Shift 1Q11If , then the value of…
Idea: Sine Product Identity with 60 Degrees
MediumSingle correct - 2 Apr, Shift 2Q13Let and…
Idea: High Power Reduction Identities
MediumSingle correct - 4 Apr, Shift 1Q23If and…
Idea: Tangent Sum/Difference to Sine Ratio
New ideaMediumNumerical value - 5 Apr, Shift 1Q6Let , , where , be the roots of the quadratic equation…
Idea: Compound Angle Formulas
MediumSingle correct - 8 Apr, Shift 2Q22If…
Idea: Tangent and Cotangent Difference Identities
New ideaHardNumerical value
JEE Main 20252 questions in 2 shifts
- 4 Apr, Shift 2Q3Let the product of and be ,…
Idea: Extrema of Quadratic Trigonometric Forms
New ideaHardSingle correct - 7 Apr, Shift 1Q1If for , the points…
Idea: Elimination of Trigonometric Parameters
New ideaMediumSingle correct
JEE Main 20245 questions in 5 shifts
- 8 Apr, Shift 2Q20If the value of is , where a, b, c are…
Idea: Values of Non-Standard Specific Angles
MediumSingle correct - 9 Apr, Shift 1Q20Let , . Then, the sum of all…
Idea: Cosine Product Identity with 60 Degrees
New ideaMediumSingle correct - 9 Apr, Shift 2Q1Let the range of the function be . If and are respectively…
Idea: Extrema of Linear Trigonometric Forms
MediumSingle correct - 27 Jan, Shift 1Q30Let the set of all such that the equation has a solution be and…
Idea: Values of Non-Standard Specific Angles
HardNumerical value - 30 Jan, Shift 2Q11For , let and a real number be such that…
Idea: Compound Angle Formulas
MediumSingle correct
JEE Main 20233 questions in 3 shifts
- 6 Apr, Shift 2Q30The value of is ___________.
Idea: Products of Tangents of Complementary Angles
New ideaHardNumerical value - 8 Apr, Shift 2Q19The value of is
Idea: Triple Angle Formulas
HardSingle correct - 10 Apr, Shift 1Q19is equal to
Idea: Product of Cosines with Doubling Angles
Asked the year beforeMediumSingle correct
JEE Main 20228 questions in 8 shifts
- 25 Jul, Shift 2Q19…
Idea: Product of Cosines with Doubling Angles
New ideaHardSingle correct - 27 Jul, Shift 2Q19Let…
Idea: Telescopic Trigonometric Series
New ideaHardSingle correct - 25 Jun, Shift 2Q15The value of is :
Idea: Values of Non-Standard Specific Angles
Asked the year beforeMediumSingle correct - 26 Jun, Shift 1Q26If , then…
Idea: Sine Product Identity with 60 Degrees
New ideaHardNumerical value - 26 Jun, Shift 2Q18is equal to :
Idea: Sine Product Identity with 60 Degrees
New ideaEasySingle correct - 27 Jun, Shift 1Q18The value of is equal to :
Idea: Trigonometric Sums via Roots of Unity
New ideaMediumSingle correct - 27 Jun, Shift 2Q19is a root of which of the following equation?
Idea: Values of Non-Standard Specific Angles
Asked the year beforeHardSingle correct - 28 Jun, Shift 2Q20If and , where and , then the value of…
Idea: Compound Angle Formulas
Asked the year beforeEasySingle correct
JEE Main 202110 questions in 9 shifts
- 3 Aug, Shift 2Q79The maximum value of under the restrictions…
Idea: Trigonometric Bounds and Inequalities
New ideaHardSingle correct - 4 Aug, Shift 1Q66The value of…
Idea: Trigonometric Series with Angles in AP
New ideaHardSingle correct - 4 Aug, Shift 1Q90If is equal to the integral solution of the inequality and is equal to the slope of the angle bisector…
Idea: Compound Angle Formulas
Asked the year beforeMediumNumerical value - 26 Aug, Shift 2Q80The value of…
Idea: Product to Sum Formulas
Asked the year beforeMediumSingle correct - 31 Aug, Shift 1Q77is a root of the equation :
Idea: Values of Non-Standard Specific Angles
New ideaMediumSingle correct - 25 Feb, Shift 2Q77If and , then is equal to :
Idea: Trigonometric Bounds and Inequalities
New ideaMediumSingle correct - 25 Jul, Shift 2Q73The value of is :
Idea: Values of Non-Standard Specific Angles
New ideaMediumSingle correct - 16 Mar, Shift 2Q77The maximum value of…
Idea: Extrema of Linear Trigonometric Forms
New ideaMediumSingle correct - 17 Mar, Shift 2Q82Let , and ; , be the slopes of three…
Idea: Triple Angle Formulas
New ideaHardNumerical value - 18 Mar, Shift 2Q61If , for some , then the value of is…
Idea: High Power Reduction Identities
New ideaMediumSingle correct
JEE Main 20202 questions in 2 shifts
- 8 Jan, Shift 2Q75If and ,…
Idea: Compound Angle Formulas
New ideaMediumNumerical value - 9 Jan, Shift 1Q69The value of…
Idea: Product to Sum Formulas
New ideaMediumSingle correct
JEE Main 20171 question in 1 shift
- 2 Apr (offline)Q88If , then the value of is :
Idea: Multiple Angle Formulas
MediumSingle correct
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.