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Previous year question hub

Trigonometric Functions And Equations - Trigonometry - Mathematics Previous Year Questions

Practice Trigonometric Functions And Equations - Trigonometry - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

61Papers
12Years
63Questions
1Topics

Trigonometric Functions And Equations question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Trigonometric Functions And Equations. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 53 84.1%
Hard 7 11.1%
Easy 3 4.8%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

Multiple Choices 46 73%
Numerical Answer Type (NAT) 17 27%

Subject weightage

Top subjects by unique question coverage.

Mathematics
63 Qs

Most asked topics

Top topics across the included previous year papers.

Trigonometry
63 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Trigonometric Functions And Equations
63 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

JEE Main 2026 (Online) 2nd April Morning Shift
1 Qs
JEE Main 2026 (Online) 5th April Evening Shift
1 Qs
JEE Main 2026 (Online) 5th April Morning Shift
1 Qs
JEE Main 2026 (Online) 6th April Morning Shift
1 Qs
JEE MAIN 2026 ONLINE 23RD JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 24TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 22ND JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 2ND APRIL EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 2ND APRIL MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 3RD APRIL EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 3RD APRIL MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 7TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 1ST FEBRUARY EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 27TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 29TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 29TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 30TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 4TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 5TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 9TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 10TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 11TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 24TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 25TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 29TH JUNE MORNING SHIFT
2 Qs
JEE MAIN 2022 ONLINE 24TH JUNE EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 24TH JUNE MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 25TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 25TH JUNE MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 26TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 26TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 27TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 27TH JUNE EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 28TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 29TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 29TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 29TH JUNE EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 30TH JUNE MORNING SHIFT
1 Qs
JEE Main 2021 (Online) 25th February Morning Shift
1 Qs
JEE Main 2021 (Online) 26th February Morning Shift
1 Qs
JEE MAIN 2021 ONLINE 16TH MARCH MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 17TH MARCH EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 18TH MARCH MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 1ST SEPTEMBER EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 22TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 25TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 26TH AUGUST MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 27TH AUGUST EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 31ST AUGUST EVENING SHIFT
1 Qs
JEE MAIN 2019 ONLINE 12TH APRIL EVENING SLOT
2 Qs
JEE MAIN 2019 ONLINE 10TH JANUARY MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 12TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 9TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 9TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2018 OFFLINE
1 Qs
JEE MAIN 2018 ONLINE 15TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2016 OFFLINE
1 Qs
JEE MAIN 2016 ONLINE 9TH APRIL MORNING SLOT
1 Qs
IIT-JEE 2007
1 Qs
AIEEE 2006
1 Qs
AIEEE 2002
1 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
JEE Main 2026 (Online) 2nd April Morning Shift20261View paper
JEE Main 2026 (Online) 5th April Evening Shift20261View paper
JEE Main 2026 (Online) 5th April Morning Shift20261View paper
JEE Main 2026 (Online) 6th April Morning Shift20261View paper
JEE MAIN 2026 ONLINE 23RD JANUARY MORNING SHIFT20261View paper
JEE MAIN 2026 ONLINE 24TH JANUARY EVENING SHIFT20261View paper
JEE MAIN 2025 ONLINE 22ND JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 2ND APRIL EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 2ND APRIL MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 3RD APRIL EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 3RD APRIL MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 7TH APRIL EVENING SHIFT20251View paper
JEE MAIN 2024 ONLINE 1ST FEBRUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 27TH JANUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 29TH JANUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 29TH JANUARY MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 30TH JANUARY MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 4TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 5TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 9TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2023 ONLINE 10TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 11TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 24TH JANUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 25TH JANUARY EVENING SHIFT20231View paper
JEE MAIN 2022 ONLINE 24TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 24TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 25TH JULY MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 25TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 26TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 26TH JULY MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 27TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 27TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 28TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 29TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 29TH JULY MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 29TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 29TH JUNE MORNING SHIFT20222View paper
JEE MAIN 2022 ONLINE 30TH JUNE MORNING SHIFT20221View paper
JEE Main 2021 (Online) 25th February Morning Shift20211View paper
JEE Main 2021 (Online) 26th February Morning Shift20211View paper
JEE MAIN 2021 ONLINE 16TH MARCH MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 17TH MARCH EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 18TH MARCH MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 1ST SEPTEMBER EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 22TH JULY EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 25TH JULY MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 26TH AUGUST MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 27TH AUGUST EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 31ST AUGUST EVENING SHIFT20211View paper
JEE MAIN 2019 ONLINE 10TH JANUARY MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 12TH APRIL EVENING SLOT20192View paper
JEE MAIN 2019 ONLINE 12TH APRIL MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 9TH APRIL MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 9TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2018 OFFLINE20181View paper
JEE MAIN 2018 ONLINE 15TH APRIL EVENING SLOT20181View paper
JEE MAIN 2016 OFFLINE20161View paper
JEE MAIN 2016 ONLINE 9TH APRIL MORNING SLOT20161View paper
IIT-JEE 200720071View paper
AIEEE 200620061View paper
AIEEE 200220021View paper

All Trigonometric Functions And Equations previous year questions

Practice every matching question in batches of 20, with every available option.

1
2002 · Mathematics · Trigonometry · Trigonometric Functions And Equations
AIEEE 2002
The number of solution of \(\tan \,x + \sec \,x = 2\cos \,x\) in \(\left[ {0,\,2\,\pi } \right]\) is
A
2
B
3
C
0
D
1
Open complete paper
2
2006 · Mathematics · Trigonometry · Trigonometric Functions And Equations
AIEEE 2006
The number of values of \(x\) in the interval \(\left[ {0,3\pi } \right]\,\) satisfying the equation \(2{\sin ^2}x + 5\sin x - 3 = 0\) is
A
4
B
6
C
1
D
2
Open complete paper
3
2016 · Mathematics · Trigonometry · Trigonometric Functions And Equations
JEE MAIN 2016 OFFLINE
If \(0 \le x < 2\pi\), then the number of real values of \(x\), which satisfy the equation \(\,\cos x + \cos 2x + \cos 3x + \cos 4x = 0\) is:
A
7
B
9
C
3
D
5
Open complete paper
4
2016 · Mathematics · Trigonometry · Trigonometric Functions And Equations
JEE MAIN 2016 ONLINE 9TH APRIL MORNING SLOT
The number of x \(\in\) [0,   2\(\pi\) ] for which

\(\left| {\sqrt {2{{\sin }^4}x + 18{{\cos }^2}x} - \sqrt {2{{\cos }^4}x + 18{{\sin }^2}x} } \right| = 1\) is :
A
2
B
4
C
6
D
8
Open complete paper
5
2018 · Mathematics · Trigonometry · Trigonometric Functions And Equations
JEE MAIN 2018 OFFLINE
If sum of all the solutions of the equation

$$8\cos x.\left( {\cos \left( {{\pi \over 6} + x} \right).\cos \left( {{\pi \over 6} - x} \right) - {1 \over 2}} \right) = 1$$

in [0, \(\pi\)] is k\(\pi\), then k is equal to
A
\({{20} \over 9}\)
B
\({2 \over 3}\)
C
\({{13} \over 9}\)
D
\({{8} \over 9}\)
Open complete paper
6
2018 · Mathematics · Trigonometry · Trigonometric Functions And Equations
JEE MAIN 2018 ONLINE 15TH APRIL EVENING SLOT
The number of solutions of sin3x = cos 2x, in the interval \(\left( {{\pi \over 2},\pi } \right)\) is :
A
1
B
2
C
3
D
4
Open complete paper
7
2019 · Mathematics · Trigonometry · Trigonometric Functions And Equations
JEE MAIN 2019 ONLINE 10TH JANUARY MORNING SLOT
The sum of all values of \(\theta\) \(\in\)\(\left( {0,{\pi \over 2}} \right)\) satisfying
sin2 2\(\theta\) + cos4 2\(\theta\) = \({3 \over 4}\) is -
A
\({{5\pi } \over 4}\)
B
\({\pi \over 2}\)
C
\(\pi\)
D
\({{3\pi } \over 8}\)
Open complete paper
8
2019 · Mathematics · Trigonometry · Trigonometric Functions And Equations
JEE MAIN 2019 ONLINE 12TH APRIL EVENING SLOT
Let S be the set of all \(\alpha\) \(\in\) R such that the equation, cos2x + \(\alpha\)sinx = 2\(\alpha\)– 7 has a solution. Then S is equal to :
A
[2, 6]
B
[3, 7]
C
[1, 4]
D
R
Open complete paper
9
2019 · Mathematics · Trigonometry · Trigonometric Functions And Equations
JEE MAIN 2019 ONLINE 12TH APRIL EVENING SLOT
If [x] denotes the greatest integer \(\le\) x, then the system of linear equations [sin \(\theta\)]x + [–cos\(\theta\)]y = 0, [cot\(\theta\)]x + y = 0
A
has a unique solution if \(\theta \in \left( {{\pi \over 2},{{2\pi } \over 3}} \right)\) and have infinitely many solutions if \(\theta \in \left( {\pi ,{{7\pi } \over 6}} \right)\)
B
have infinitely many solutions if \(\theta \in \left( {{\pi \over 2},{{2\pi } \over 3}} \right)\) and has a unique solution if \(\theta \in \left( {\pi ,{{7\pi } \over 6}} \right)\)
C
have infinitely many solutions if \(\theta \in \left( {{\pi \over 2},{{2\pi } \over 3}} \right) \cup \left( {\pi ,{{7\pi } \over 6}} \right)\)
D
has a unique solution if \(\theta \in \left( {{\pi \over 2},{{2\pi } \over 3}} \right) \cup \left( {\pi ,{{7\pi } \over 6}} \right)\)
Open complete paper
10
2019 · Mathematics · Trigonometry · Trigonometric Functions And Equations
JEE MAIN 2019 ONLINE 12TH APRIL MORNING SLOT
The number of solutions of the equation
1 + sin4 x = cos23x, \(x \in \left[ { - {{5\pi } \over 2},{{5\pi } \over 2}} \right]\) is :
A
5
B
3
C
7
D
4
Open complete paper
11
2019 · Mathematics · Trigonometry · Trigonometric Functions And Equations
JEE MAIN 2019 ONLINE 9TH APRIL MORNING SLOT
Let S = {\(\theta\) \(\in\) [–2\(\pi\), 2\(\pi\)] : 2cos2\(\theta\) + 3sin\(\theta\) = 0}. Then the sum of the elements of S is
A
\(\pi\)
B
2\(\pi\)
C
\({{13\pi } \over 6}\)
D
\({{5\pi } \over 3}\)
Open complete paper
12
2019 · Mathematics · Trigonometry · Trigonometric Functions And Equations
JEE MAIN 2019 ONLINE 9TH JANUARY EVENING SLOT
If  0 \(\le\) x < \({\pi \over 2}\),  then the number of values of x for which sin x \(-\) sin 2x + sin 3x = 0, is :
A
3
B
1
C
4
D
2
Open complete paper
13
2021 · Mathematics · Trigonometry · Trigonometric Functions And Equations
JEE MAIN 2021 ONLINE 16TH MARCH MORNING SHIFT
The number of roots of the equation, (81)sin2x + (81)cos2x = 30 in the interval [ 0, \(\pi\) ] is equal to :
A
2
B
3
C
4
D
8
Open complete paper
14
2021 · Mathematics · Trigonometry · Trigonometric Functions And Equations
JEE MAIN 2021 ONLINE 17TH MARCH EVENING SHIFT
The number of solutions of the equation x + 2tanx = \({\pi \over 2}\) in the interval [0, 2\(\pi\)] is :
A
4
B
3
C
2
D
5
Open complete paper
15
2021 · Mathematics · Trigonometry · Trigonometric Functions And Equations
JEE MAIN 2021 ONLINE 18TH MARCH MORNING SHIFT
The number of solutions of the equation

\(|\cot x| = \cot x + {1 \over {\sin x}}\) in the interval [ 0, 2\(\pi\) ] is
Enter a numerical response
Open complete paper
16
2021 · Mathematics · Trigonometry · Trigonometric Functions And Equations
JEE MAIN 2021 ONLINE 1ST SEPTEMBER EVENING SHIFT
If n is the number of solutions of the equation
\(2\cos x\left( {4\sin \left( {{\pi \over 4} + x} \right)\sin \left( {{\pi \over 4} - x} \right) - 1} \right) = 1,x \in [0,\pi ]\) and S is the sum of all these solutions, then the ordered pair (n, S) is :
A
(3, 13\(\pi\) / 9)
B
(2, 2\(\pi\) / 3)
C
(2, 8\(\pi\) / 9)
D
(3, 5\(\pi\) / 3)
Open complete paper
17
2021 · Mathematics · Trigonometry · Trigonometric Functions And Equations
JEE MAIN 2021 ONLINE 22TH JULY EVENING SHIFT
The number of solutions of sin7x + cos7x = 1, x\(\in\) [0, 4\(\pi\)] is equal to
A
11
B
7
C
5
D
9
Open complete paper
18
2021 · Mathematics · Trigonometry · Trigonometric Functions And Equations
JEE MAIN 2021 ONLINE 25TH JULY MORNING SHIFT
The sum of all values of x in [0, 2\(\pi\)], for which sin x + sin 2x + sin 3x + sin 4x = 0, is equal to :
A
8\(\pi\)
B
11\(\pi\)
C
12\(\pi\)
D
9\(\pi\)
Open complete paper
19
2021 · Mathematics · Trigonometry · Trigonometric Functions And Equations
JEE MAIN 2021 ONLINE 26TH AUGUST MORNING SHIFT
The sum of solutions of the equation

\({{\cos x} \over {1 + \sin x}} = \left| {\tan 2x} \right|\), \(x \in \left( { - {\pi \over 2},{\pi \over 2}} \right) - \left\{ {{\pi \over 4}, - {\pi \over 4}} \right\}\) is :
A
\(- {{11\pi } \over {30}}\)
B
\({\pi \over {10}}\)
C
\(- {{7\pi } \over {30}}\)
D
\(- {\pi \over {15}}\)
Open complete paper
20
2021 · Mathematics · Trigonometry · Trigonometric Functions And Equations
JEE MAIN 2021 ONLINE 27TH AUGUST EVENING SHIFT
Let S be the sum of all solutions (in radians) of the equation \({\sin ^4}\theta + {\cos ^4}\theta - \sin \theta \cos \theta = 0\) in [0, 4\(\pi\)]. Then \({{8S} \over \pi }\) is equal to ____________.
Enter a numerical response
Open complete paper

Showing 20 of 63 questions