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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.

56Papers
45Years
99Questions
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 58 57.4%
Easy 21 20.8%
Hard 19 18.8%
Not classified 3 3%

Question type distribution

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

Multiple Choices 63 62.4%
Subjective 20 19.8%
Numerical Answer Type (NAT) 11 10.9%
Fill in the blanks 7 6.9%

Subject weightage

Top subjects by unique question coverage.

Mathematics
99 Qs

Most asked topics

Top topics across the included previous year papers.

Trigonometry
99 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Trigonometric Functions And Equations
99 Qs

Paper coverage

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

JEE Advanced 2026 Paper 1 Online
1 Qs
JEE Advanced 2026 Paper 1 Online
1 Qs
JEE Advanced 2026 Paper 1 Online
1 Qs
JEE Advanced 2026 Paper 2 Online
1 Qs
JEE ADVANCED 2025 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2024 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2023 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2022 PAPER 2 ONLINE
2 Qs
JEE ADVANCED 2022 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2019 PAPER 2 OFFLINE
3 Qs
JEE ADVANCED 2018 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2018 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2017 PAPER 2 OFFLINE
2 Qs
JEE ADVANCED 2016 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2016 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2015 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2014 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2013 PAPER 1 OFFLINE
2 Qs
IIT JEE 2012 PAPER 1 OFFLINE
1 Qs
IIT JEE 2011 PAPER 1 OFFLINE
2 Qs
IIT JEE 2010 PAPER 1 OFFLINE
3 Qs
IIT JEE 2010 PAPER 2 OFFLINE
1 Qs
IIT JEE 2009 PAPER 2 OFFLINE
2 Qs
IIT JEE 2009 PAPER 1 OFFLINE
1 Qs
IIT JEE 2008 PAPER 2 OFFLINE
1 Qs
IIT JEE 2007 PAPER 1 OFFLINE
1 Qs
IIT JEE 2006
2 Qs
IIT JEE 2005
1 Qs
IIT JEE 2005 SCREENING
1 Qs
IIT JEE 2004 SCREENING
1 Qs
IIT JEE 2002 SCREENING
1 Qs
IIT JEE 2001 SCREENING
3 Qs
IIT JEE 2000
1 Qs
IIT JEE 2000 SCREENING
1 Qs
IIT JEE 1999
2 Qs
IIT JEE 1998
3 Qs
IIT JEE 1997
3 Qs
IIT JEE 1996
3 Qs
IIT JEE 1995
2 Qs
IIT JEE 1995 SCREENING
2 Qs
IIT JEE 1994
4 Qs
IIT JEE 1993
4 Qs
IIT JEE 1992
2 Qs
IIT JEE 1991
2 Qs
IIT JEE 1990
2 Qs
IIT JEE 1989
1 Qs
IIT JEE 1988
2 Qs
IIT JEE 1987
4 Qs
IIT JEE 1986
1 Qs
IIT JEE 1984
3 Qs
IIT JEE 1983
3 Qs
IIT JEE 1982
1 Qs
IIT JEE 1981
2 Qs
IIT JEE 1980
5 Qs
IIT JEE 1979
3 Qs
IIT JEE 1978
1 Qs

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
JEE Advanced 2026 Paper 1 Online20261View paper
JEE Advanced 2026 Paper 1 Online20261View paper
JEE Advanced 2026 Paper 1 Online20261View paper
JEE Advanced 2026 Paper 2 Online20261View paper
JEE ADVANCED 2025 PAPER 2 ONLINE20251View paper
JEE ADVANCED 2024 PAPER 1 ONLINE20241View paper
JEE ADVANCED 2023 PAPER 2 ONLINE20231View paper
JEE ADVANCED 2022 PAPER 1 ONLINE20221View paper
JEE ADVANCED 2022 PAPER 2 ONLINE20222View paper
JEE ADVANCED 2019 PAPER 2 OFFLINE20193View paper
JEE ADVANCED 2018 PAPER 1 OFFLINE20181View paper
JEE ADVANCED 2018 PAPER 2 OFFLINE20181View paper
JEE ADVANCED 2017 PAPER 2 OFFLINE20172View paper
JEE ADVANCED 2016 PAPER 1 OFFLINE20161View paper
JEE ADVANCED 2016 PAPER 2 OFFLINE20161View paper
JEE ADVANCED 2015 PAPER 1 OFFLINE20151View paper
JEE ADVANCED 2014 PAPER 2 OFFLINE20141View paper
JEE ADVANCED 2013 PAPER 1 OFFLINE20132View paper
IIT JEE 2012 PAPER 1 OFFLINE20121View paper
IIT JEE 2011 PAPER 1 OFFLINE20112View paper
IIT JEE 2010 PAPER 1 OFFLINE20103View paper
IIT JEE 2010 PAPER 2 OFFLINE20101View paper
IIT JEE 2009 PAPER 1 OFFLINE20091View paper
IIT JEE 2009 PAPER 2 OFFLINE20092View paper
IIT JEE 2008 PAPER 2 OFFLINE20081View paper
IIT JEE 2007 PAPER 1 OFFLINE20071View paper
IIT JEE 200620062View paper
IIT JEE 200520051View paper
IIT JEE 2005 SCREENING20051View paper
IIT JEE 2004 SCREENING20041View paper
IIT JEE 2002 SCREENING20021View paper
IIT JEE 2001 SCREENING20013View paper
IIT JEE 200020001View paper
IIT JEE 2000 SCREENING20001View paper
IIT JEE 199919992View paper
IIT JEE 199819983View paper
IIT JEE 199719973View paper
IIT JEE 199619963View paper
IIT JEE 199519952View paper
IIT JEE 1995 SCREENING19952View paper
IIT JEE 199419944View paper
IIT JEE 199319934View paper
IIT JEE 199219922View paper
IIT JEE 199119912View paper
IIT JEE 199019902View paper
IIT JEE 198919891View paper
IIT JEE 198819882View paper
IIT JEE 198719874View paper
IIT JEE 198619861View paper
IIT JEE 198419843View paper
IIT JEE 198319833View paper
IIT JEE 198219821View paper
IIT JEE 198119812View paper
IIT JEE 198019805View paper
IIT JEE 197919793View paper
IIT JEE 197819781View paper

All Trigonometric Functions And Equations previous year questions

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

1
1978 · Mathematics · Trigonometry · Trigonometric Functions And Equations
IIT JEE 1978
If \(\tan \alpha = {m \over {m + 1}}\,\) and \(\tan \beta = {2 \over {2m + 1}},\) find the possible values of \(\left( {\alpha + \beta } \right).\)
Write your response
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2
1979 · Mathematics · Trigonometry · Trigonometric Functions And Equations
IIT JEE 1979
If \(\tan \theta = - {4 \over 3},then\sin \theta \,is\,\)
A
\(- {4 \over 5}\,but\,not\,{4 \over 5}\)
B
\(- {4 \over 5}\,or\,{4 \over 5}\)
C
\({4 \over 5}\,\,but\,not\, - {4 \over 5}\)
D
None of these.
Open complete paper
3
1979 · Mathematics · Trigonometry · Trigonometric Functions And Equations
IIT JEE 1979
If \(\alpha + \beta + \gamma = 2\pi ,\) then
A
\(tan{\alpha \over 2} + \tan {\beta \over 2} + \tan {\gamma \over 2} = \tan {\alpha \over 2}\tan {\beta \over 2}\tan {\gamma \over 2}\)
B
\(\tan {\alpha \over 2}\tan {\beta \over 2} + \tan {\beta \over 2}\tan {\gamma \over 2} + \tan {\gamma \over 2}\tan {\alpha \over 2} = 1\)
C
\(tan{\alpha \over 2} + \tan {\beta \over 2} + \tan {\gamma \over 2} = - \tan {\alpha \over 2}\tan {\beta \over 2}\tan {\gamma \over 2}\)
D
None of these.
Open complete paper
4
1979 · Mathematics · Trigonometry · Trigonometric Functions And Equations
IIT JEE 1979
(a) Draw the graph of \(y = {1 \over {\sqrt 2 }}\left( {cinx + \cos x} \right)\) from \(x = - {\pi \over 2}\) to \(x = {\pi \over 2}\).

(b) If \(\cos \left( {\alpha + \beta } \right) = {4 \over 5},\,\,\sin \,\left( {\alpha - \beta } \right) = \,{5 \over {13}},\) and \(\alpha ,\,\beta\) lies between 0 and \({\pi \over 4}\), find tan2\(\alpha\).

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5
1980 · Mathematics · Trigonometry · Trigonometric Functions And Equations
IIT JEE 1980
Given \(\alpha + \beta - \gamma = \pi ,\) prove that
$$\,{\sin ^2}\alpha + {\sin ^2}\beta - {\sin ^2}\gamma = 2\sin \alpha {\mkern 1mu} \sin \beta {\mkern 1mu} \cos y$$
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6
1980 · Mathematics · Trigonometry · Trigonometric Functions And Equations
IIT JEE 1980
For all \(\theta\) in \(\left[ {0,\,\pi /2} \right]\) show that, \(\cos \left( {\sin \theta } \right) \ge \,\sin \,\left( {\cos \theta } \right).\)
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7
1980 · Mathematics · Trigonometry · Trigonometric Functions And Equations
IIT JEE 1980
The equation \(\,2{\cos ^2}{x \over 2}{\sin ^2}x = {x^2} + {x^{ - 2}};\,0 < x \le {\pi \over 2}\) has
A
no real solution
B
one real solution
C
more than one solution
D
none of these
Open complete paper
8
1980 · Mathematics · Trigonometry · Trigonometric Functions And Equations
IIT JEE 1980
Given \(A = {\sin ^2}\theta + {\cos ^4}\theta\) then for all real values of \(\theta\)
A
\(1 \le A \le 2\)
B
\({3 \over 4} \le A \le 1\)
C
\({13\over 16} \le A \le 1\)
D
\({3 \over 4} \le A \le {{13} \over {16}}\)
Open complete paper
9
1980 · Mathematics · Trigonometry · Trigonometric Functions And Equations
IIT JEE 1980
Given \(A = \left\{ {x:{\pi \over 6} \le x \le {\pi \over 3}} \right\}\) and
\(f\left( x \right) = \cos x - x\left( {1 + x} \right);\) find \(f\left( A \right).\)
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10
1981 · Mathematics · Trigonometry · Trigonometric Functions And Equations
IIT JEE 1981
Suppose \({\sin ^3}\,x\sin 3x = \sum\limits_{m = 0}^n {{C_m}\cos \,mx}\) is an identity in x, where C0, C1 ,....Cn are constants, and \({C_n} \ne 0\) , then the value of n is _____.
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11
1981 · Mathematics · Trigonometry · Trigonometric Functions And Equations
IIT JEE 1981
The general solution of the trigonometric equation sin x+cos x=1 is given by:
A
\(2n\pi ;\,n = 0,\, \pm 1,\, \pm 2....\)
B
\(x = 2n\pi + \pi /2;\,n = 0,\, \pm 1,\, \pm 2....\)
C
\(x = n\pi + {\left( { - 1} \right)^n}\,\,\,\,\,\,\,{\pi \over 4} - {\pi \over 4}\) ; \(n = 0,\, \pm 1,\, \pm 2..\)
D
none of these
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12
1982 · Mathematics · Trigonometry · Trigonometric Functions And Equations
IIT JEE 1982
Without using tables, prove that \(\left( {\sin \,{{12}^ \circ }} \right)\left( {\sin \,{{48}^ \circ }} \right)\left( {\sin \,{{54}^ \circ }} \right) = {1 \over 8}.\)
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13
1983 · Mathematics · Trigonometry · Trigonometric Functions And Equations
IIT JEE 1983
If \(\tan \,A = \left( {1 - \cos B} \right)/\sin B,\) then \(tan2A = tan\,B\).
A
TRUE
B
FALSE
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14
1983 · Mathematics · Trigonometry · Trigonometric Functions And Equations
IIT JEE 1983
Show that \(16\cos \left( {{{2\pi } \over {15}}} \right)\cos \left( {{{4\pi } \over {15}}} \right)\cos \left( {{{8\pi } \over {15}}} \right)\cos \left( {{{16\pi } \over {15}}} \right) = 1\)
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15
1983 · Mathematics · Trigonometry · Trigonometric Functions And Equations
IIT JEE 1983
Find all solutions of \(4{\cos ^2}\,x\sin x - 2{\sin ^2}x = 3\sin x\)
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16
1984 · Mathematics · Trigonometry · Trigonometric Functions And Equations
IIT JEE 1984
There exists a value of \(\theta\) between 0 and \(2\pi\) that satisfies the equation \(\,\,{\sin ^4}\theta - 2{\sin ^2}\theta - 1 = 0.\)
A
TRUE
B
FALSE
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17
1984 · Mathematics · Trigonometry · Trigonometric Functions And Equations
IIT JEE 1984
\(\left( {1 + \cos {\pi \over 8}} \right)\left( {1 + \cos {{3\pi } \over 8}} \right)\left( {1 + \cos {{5\pi } \over 8}} \right)\left( {1 + \cos {{7\pi } \over 8}} \right)\) is equal to
A
\({1 \over 2}\)
B
\(\cos {\pi \over 8}\)
C
\({1 \over 8}\)
D
\({{1 + \sqrt 2 } \over {2\sqrt 2 }}\)
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18
1984 · Mathematics · Trigonometry · Trigonometric Functions And Equations
IIT JEE 1984
Find the values of \(x \in \left( { - \pi , + \pi } \right)\) which satisfy the equation \({g^{(1 + \left| {\cos x} \right| + \left| {{{\cos }^2}x} \right| + \left| {{{\cos }^3}x} \right| + ...)}} = {4^3}\)
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19
1986 · Mathematics · Trigonometry · Trigonometric Functions And Equations
IIT JEE 1986
The expression \(2\left[ {{{\sin }^6}\left( {{\pi \over 2} + \alpha } \right) + {{\sin }^6}\left( {5\pi - \alpha } \right)} \right]\) is equal to
A
0
B
1
C
3
D
\(\sin \,4\,\alpha + \cos \,6\,\alpha \,\,\,\,\)
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20
1987 · Mathematics · Trigonometry · Trigonometric Functions And Equations
IIT JEE 1987
The solution set of the system of equations \(X + Y = {{2\pi } \over 3},\) \(cox\,x + cos\,y = {3 \over 2},\) where x and y are real, is _____.
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Showing 20 of 99 questions