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Previous year question hub

Trigonometric Ratio And Identites - Trigonometry - Mathematics Previous Year Questions

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

66Papers
17Years
69Questions
1Topics

Trigonometric Ratio And Identites question pattern

Every graph below is calculated only from this selection.

Questions by year

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

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 57 82.6%
Easy 6 8.7%
Hard 6 8.7%

Question type distribution

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

Multiple Choices 60 87%
Numerical Answer Type (NAT) 9 13%

Subject weightage

Top subjects by unique question coverage.

Mathematics
69 Qs

Most asked topics

Top topics across the included previous year papers.

Trigonometry
69 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Trigonometric Ratio And Identites
69 Qs

Paper coverage

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

JEE Main 2026 (Online) 4th April Morning Shift
2 Qs
JEE MAIN 2026 ONLINE 24TH JANUARY MORNING SHIFT
2 Qs
JEE Main 2026 (Online) 2nd April Evening Shift
1 Qs
JEE Main 2026 (Online) 2nd April Morning Shift
1 Qs
JEE Main 2026 (Online) 5th April Morning Shift
1 Qs
JEE MAIN 2026 ONLINE 21ST JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 22ND JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 22ND JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 23RD JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 28TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 23RD JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 23RD JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 28TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 29TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 4TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 7TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 1ST FEBRUARY MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 27TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 30TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 31ST JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 5TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 8TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 8TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 10TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 29TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 29TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 30TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 6TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 8TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 25TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 25TH JUNE EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 26TH JUNE EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 26TH JUNE MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 27TH JUNE EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 27TH JUNE MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 28TH JUNE EVENING SHIFT
1 Qs
JEE Main 2021 (Online) 24th February Morning Shift
1 Qs
JEE Main 2021 (Online) 25th February Evening 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 18TH MARCH EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 25TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 26TH AUGUST EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 27TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 27TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2020 ONLINE 2ND SEPTEMBER EVENING SLOT
1 Qs
JEE MAIN 2020 ONLINE 5TH SEPTEMBER EVENING SLOT
1 Qs
JEE MAIN 2020 ONLINE 8TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2020 ONLINE 9TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2020 ONLINE 9TH JANUARY MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 10TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 12TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 12TH JANUARY MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 8TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 9TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 9TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 9TH JANUARY MORNING SLOT
1 Qs
JEE MAIN 2017 OFFLINE
1 Qs
JEE MAIN 2016 ONLINE 9TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2014 OFFLINE
1 Qs
JEE MAIN 2013 OFFLINE
1 Qs
AIEEE 2011
1 Qs
AIEEE 2010
1 Qs
AIEEE 2009
1 Qs
AIEEE 2006
1 Qs
AIEEE 2004
2 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 Evening Shift20261View paper
JEE Main 2026 (Online) 2nd April Morning Shift20261View paper
JEE Main 2026 (Online) 4th April Morning Shift20262View paper
JEE Main 2026 (Online) 5th April Morning Shift20261View paper
JEE MAIN 2026 ONLINE 21ST JANUARY MORNING SHIFT20261View paper
JEE MAIN 2026 ONLINE 22ND JANUARY EVENING SHIFT20261View paper
JEE MAIN 2026 ONLINE 22ND JANUARY MORNING SHIFT20261View paper
JEE MAIN 2026 ONLINE 23RD JANUARY EVENING SHIFT20261View paper
JEE MAIN 2026 ONLINE 24TH JANUARY MORNING SHIFT20262View paper
JEE MAIN 2026 ONLINE 28TH JANUARY MORNING SHIFT20261View paper
JEE MAIN 2025 ONLINE 23RD JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 23RD JANUARY MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 28TH JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 29TH JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 4TH APRIL MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 7TH APRIL MORNING SHIFT20251View paper
JEE MAIN 2024 ONLINE 1ST FEBRUARY MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 27TH JANUARY MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 30TH JANUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 31ST JANUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 5TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 8TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 8TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2023 ONLINE 10TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 29TH JANUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 29TH JANUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 30TH JANUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 6TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 8TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2022 ONLINE 25TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 25TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 26TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 26TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 27TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 27TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 28TH JUNE EVENING SHIFT20221View paper
JEE Main 2021 (Online) 24th February Morning Shift20211View paper
JEE Main 2021 (Online) 25th February Evening Shift20211View paper
JEE Main 2021 (Online) 26th February Morning Shift20211View paper
JEE MAIN 2021 ONLINE 16TH MARCH MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 18TH MARCH EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 25TH JULY EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 26TH AUGUST EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 27TH JULY EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 27TH JULY MORNING SHIFT20211View paper
JEE MAIN 2020 ONLINE 2ND SEPTEMBER EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 5TH SEPTEMBER EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 8TH JANUARY EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 9TH JANUARY EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 9TH JANUARY MORNING SLOT20201View paper
JEE MAIN 2019 ONLINE 10TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 12TH APRIL MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 12TH JANUARY MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 8TH APRIL MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 9TH APRIL EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 9TH APRIL MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 9TH JANUARY MORNING SLOT20191View paper
JEE MAIN 2017 OFFLINE20171View paper
JEE MAIN 2016 ONLINE 9TH APRIL MORNING SLOT20161View paper
JEE MAIN 2014 OFFLINE20141View paper
JEE MAIN 2013 OFFLINE20131View paper
AIEEE 201120111View paper
AIEEE 201020101View paper
AIEEE 200920091View paper
AIEEE 200620061View paper
AIEEE 200420042View paper

All Trigonometric Ratio And Identites previous year questions

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

1
2004 · Mathematics · Trigonometry · Trigonometric Ratio And Identites
AIEEE 2004
Let \(\alpha ,\,\beta\) be such that \(\pi < \alpha - \beta < 3\pi\).
If \(sin{\mkern 1mu} \alpha + \sin \beta = - {{21} \over {65}}\) and \(\cos \alpha + \cos \beta = - {{27} \over {65}}\) then the value of \(\cos {{\alpha - \beta } \over 2}\) :
A
\({{ - 6} \over {65}}\,\,\)
B
\({3 \over {\sqrt {130} }}\)
C
\({6 \over {65}}\)
D
\(- {3 \over {\sqrt {130} }}\)
Open complete paper
2
2004 · Mathematics · Trigonometry · Trigonometric Ratio And Identites
AIEEE 2004
If \(u = \sqrt {{a^2}{{\cos }^2}\theta + {b^2}{{\sin }^2}\theta } + \sqrt {{a^2}{{\sin }^2}\theta + {b^2}{{\cos }^2}\theta }\)

then the difference between the maximum and minimum values of \({u^2}\) is given by :
A
\({\left( {a - b} \right)^2}\)
B
\(2\sqrt {{a^2} + {b^2}}\)
C
\({\left( {a + b} \right)^2}\)
D
\(2\left( {{a^2} + {b^2}} \right)\)
Open complete paper
3
2006 · Mathematics · Trigonometry · Trigonometric Ratio And Identites
AIEEE 2006
If \(0 < x < \pi\) and \(\cos x + \sin x = {1 \over 2},\) then \(\tan x\) is :
A
\({{\left( {1 - \sqrt 7 } \right)} \over 4}\)
B
\({{\left( {4 - \sqrt 7 } \right)} \over 3}\)
C
\(- {{\left( {4 + \sqrt 7 } \right)} \over 3}\)
D
\({{\left( {1 + \sqrt 7 } \right)} \over 4}\)
Open complete paper
4
2009 · Mathematics · Trigonometry · Trigonometric Ratio And Identites
AIEEE 2009
Let A and B denote the statements

A: \(\cos \alpha + \cos \beta + \cos \gamma = 0\)

B: \(\sin \alpha + \sin \beta + \sin \gamma = 0\)

If \(\cos \left( {\beta - \gamma } \right) + \cos \left( {\gamma - \alpha } \right) + \cos \left( {\alpha - \beta } \right) = - {3 \over 2},\) then:

A
A is false and B is true
B
both A and B are true
C
both A and B are false
D
A is true and B is false
Open complete paper
5
2010 · Mathematics · Trigonometry · Trigonometric Ratio And Identites
AIEEE 2010
Let \(\cos \left( {\alpha + \beta } \right) = {4 \over 5}\) and \(\sin \,\,\,\left( {\alpha - \beta } \right) = {5 \over {13}},\) where \(0 \le \alpha ,\,\beta \le {\pi \over 4}.\)
Then \(tan\,2\alpha\) =
A
\({56 \over 33}\)
B
\({19 \over 12}\)
C
\({20 \over 7}\)
D
\({25 \over 16}\)
Open complete paper
6
2011 · Mathematics · Trigonometry · Trigonometric Ratio And Identites
AIEEE 2011
If \(A = {\sin ^2}x + {\cos ^4}x,\) then for all real \(x\):
A
\({{13} \over {16}} \le A \le 1\)
B
\(1 \le A \le 2\)
C
\({3 \over 4} \le A \le {{13} \over {16}}\)
D
\({{3} \over {4}} \le A \le 1\)
Open complete paper
7
2013 · Mathematics · Trigonometry · Trigonometric Ratio And Identites
JEE MAIN 2013 OFFLINE
The expression \({{\tan {\rm A}} \over {1 - \cot {\rm A}}} + {{\cot {\rm A}} \over {1 - \tan {\rm A}}}\) can be written as:
A
\(\sin {\rm A}\,\cos {\rm A} + 1\)
B
\(\sec {\rm A}\,\cos ec{\rm A} + 1\)
C
\(\tan {\rm A} + \cot {\rm A}\)
D
\(\sec {\rm A} + \cos ec{\rm A}\)
Open complete paper
8
2014 · Mathematics · Trigonometry · Trigonometric Ratio And Identites
JEE MAIN 2014 OFFLINE
Let \(f_k\left( x \right) = {1 \over k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)\) where \(x \in R\) and \(k \ge \,1.\)
Then \({f_4}\left( x \right) - {f_6}\left( x \right)\,\,\) equals :
A
\({1 \over 4}\)
B
\({1 \over 12}\)
C
\({1 \over 6}\)
D
\({1 \over 3}\)
Open complete paper
9
2016 · Mathematics · Trigonometry · Trigonometric Ratio And Identites
JEE MAIN 2016 ONLINE 9TH APRIL MORNING SLOT
If  m and M are the minimum and the maximum values of

4 + \({1 \over 2}\) sin2 2x \(-\) 2cos4 x, x \(\in\) R, then M \(-\) m is equal to :
A
\({{15} \over 4}\)
B
\({{9} \over 4}\)
C
\({{7} \over 4}\)
D
\({{1} \over 4}\)
Open complete paper
10
2017 · Mathematics · Trigonometry · Trigonometric Ratio And Identites
JEE MAIN 2017 OFFLINE
If \(5\left( {{{\tan }^2}x - {{\cos }^2}x} \right) = 2\cos 2x + 9\),

then the value of \(\cos 4x\) is :
A
\({1 \over 3}\)
B
\({2 \over 9}\)
C
\(- {7 \over 9}\)
D
\(- {3 \over 5}\)
Open complete paper
11
2019 · Mathematics · Trigonometry · Trigonometric Ratio And Identites
JEE MAIN 2019 ONLINE 10TH JANUARY EVENING SLOT
The value of \(\cos {\pi \over {{2^2}}}.\cos {\pi \over {{2^3}}}\,.....\cos {\pi \over {{2^{10}}}}.\sin {\pi \over {{2^{10}}}}\) is -
A
\({1 \over {256}}\)
B
\({1 \over {2}}\)
C
\({1 \over {1024}}\)
D
\({1 \over {512}}\)
Open complete paper
12
2019 · Mathematics · Trigonometry · Trigonometric Ratio And Identites
JEE MAIN 2019 ONLINE 12TH APRIL MORNING SLOT
The equation y = sinx sin (x + 2) – sin2 (x + 1) represents a straight line lying in :
A
first, second and fourth quadrants
B
first, third and fourth quadrants
C
second and third quadrants only
D
third and fourth quadrants only
Open complete paper
13
2019 · Mathematics · Trigonometry · Trigonometric Ratio And Identites
JEE MAIN 2019 ONLINE 12TH JANUARY MORNING SLOT
The maximum value of 3cos\(\theta\) + 5sin \(\left( {\theta - {\pi \over 6}} \right)\) for any real value of \(\theta\) is :
A
\(\sqrt {34}\)
B
\(\sqrt {31}\)
C
\(\sqrt {19}\)
D
\({{\sqrt {79} } \over 2}\)
Open complete paper
14
2019 · Mathematics · Trigonometry · Trigonometric Ratio And Identites
JEE MAIN 2019 ONLINE 8TH APRIL MORNING SLOT
If cos(\(\alpha\) + \(\beta\)) = 3/5 ,sin ( \(\alpha\) - \(\beta\)) = 5/13 and 0 < \(\alpha , \beta\) < \(\pi \over 4\), then tan(2\(\alpha\)) is equal to :
A
21/16
B
63/52
C
33/52
D
63/16
Open complete paper
15
2019 · Mathematics · Trigonometry · Trigonometric Ratio And Identites
JEE MAIN 2019 ONLINE 9TH APRIL EVENING SLOT
The value of sin 10º sin30º sin50º sin70º is :-
A
\({1 \over {36}}\)
B
\({1 \over {16}}\)
C
\({1 \over {32}}\)
D
\({1 \over {18}}\)
Open complete paper
16
2019 · Mathematics · Trigonometry · Trigonometric Ratio And Identites
JEE MAIN 2019 ONLINE 9TH APRIL MORNING SLOT
The value of cos210° – cos10°cos50° + cos250° is
A
\({3 \over 2} + \cos {20^o}\)
B
\({3 \over 4}\)
C
\({3 \over 2}(1 + \cos {20^o})\)
D
\({3 \over 2}\)
Open complete paper
17
2019 · Mathematics · Trigonometry · Trigonometric Ratio And Identites
JEE MAIN 2019 ONLINE 9TH JANUARY MORNING SLOT
For any \(\theta \in \left( {{\pi \over 4},{\pi \over 2}} \right)\), the expression

\(3{(\cos \theta - \sin \theta )^4}\)\(+ 6{(\sin \theta + \cos \theta )^2} + 4{\sin ^6}\theta\)

equals :
A
13 – 4 cos2\(\theta\) + 6sin2\(\theta\)cos2\(\theta\)
B
13 – 4 cos6\(\theta\)
C
13 – 4 cos2\(\theta\) + 6cos2\(\theta\)
D
13 – 4 cos4\(\theta\) + 2sin2\(\theta\)cos2\(\theta\)
Open complete paper
18
2020 · Mathematics · Trigonometry · Trigonometric Ratio And Identites
JEE MAIN 2020 ONLINE 2ND SEPTEMBER EVENING SLOT
If the equation cos4 \(\theta\) + sin4 \(\theta\) + \(\lambda\) = 0 has real solutions for \(\theta\), then \(\lambda\) lies in the interval :
A
\(\left[ { - {3 \over 2}, - {5 \over 4}} \right]\)
B
\(\left( { - {1 \over 2}, - {1 \over 4}} \right]\)
C
\(\left( { - {5 \over 4}, - 1} \right]\)
D
\(\left[ { - 1, - {1 \over 2}} \right]\)
Open complete paper
19
2020 · Mathematics · Trigonometry · Trigonometric Ratio And Identites
JEE MAIN 2020 ONLINE 5TH SEPTEMBER EVENING SLOT
If L = sin2\(\left( {{\pi \over {16}}} \right)\) - sin2\(\left( {{\pi \over {8}}} \right)\) and
M = cos2\(\left( {{\pi \over {16}}} \right)\) - sin2\(\left( {{\pi \over {8}}} \right)\), then :
A
L = \(- {1 \over {2\sqrt 2 }} + {1 \over 2}\cos {\pi \over 8}\)
B
M = \({1 \over {2\sqrt 2 }} + {1 \over 2}\cos {\pi \over 8}\)
C
M = \({1 \over {4\sqrt 2 }} + {1 \over 4}\cos {\pi \over 8}\)
D
L = \({1 \over {4\sqrt 2 }} - {1 \over 4}\cos {\pi \over 8}\)
Open complete paper
20
2020 · Mathematics · Trigonometry · Trigonometric Ratio And Identites
JEE MAIN 2020 ONLINE 8TH JANUARY EVENING SLOT
If \({{\sqrt 2 \sin \alpha } \over {\sqrt {1 + \cos 2\alpha } }} = {1 \over 7}\) and \(\sqrt {{{1 - \cos 2\beta } \over 2}} = {1 \over {\sqrt {10} }}\)

\(\alpha ,\beta \in \left( {0,{\pi \over 2}} \right)\) then tan(\(\alpha\) + 2\(\beta\)) is equal to _____.
Enter a numerical response
Open complete paper

Showing 20 of 69 questions