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Mathematics - Trigonometric Equations

Practise 78 JEE Main previous year questions on Trigonometric Equations, compiled from papers spanning 2002 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty JEE Main tests.

Trigonometric Equations has been asked in 16 of the 25 years of JEE Main papers analysed (2002–2026), with 78 questions in all. 18% of them were easy, 59% moderate and 23% tough. Most of its questions came from 2021, with 13 questions that year. In the last three years (2024–2026) it had 19 questions across 49 papers, about 0.4 per paper.

The chapter's 2 topics are not weighted equally: Solving Trigonometric Equation (75 questions, 96%) and Solving Trigonometric Inequalities (3 questions, 4%) have been asked the most. Solving Trigonometric Equation has also led over the last five years, with 40 questions. Solving Trigonometric Equation has produced the most tough questions (18).

  1. 1Let . Then is equal to:06 Apr, 2026 (M)Solving Trigonometric Equation
  2. 2If , then is equal to _______.05 Apr, 2026 (E)Solving Trigonometric Equation
  3. 3Let . Then is equal to :02 Apr, 2026 (M)Solving Trigonometric Equation
  4. 4The number of elements in the set is .24 Jan, 2026 (E)Solving Trigonometric Equation
  5. 5Number of solutions of is:23 Jan, 2026 (M)Solving Trigonometric Equation
  6. 6If for , the points lie on , then is equal to :07 Apr, 2025 (M)Solving Trigonometric Equation
  7. 7The number of solutions of the equation in is :07 Apr, 2025 (E)Solving Trigonometric Equation
  8. 8If , then the value of is:04 Apr, 2025 (M)Solving Trigonometric Equation
  9. 9The number of solutions of the equation is03 Apr, 2025 (M)Solving Trigonometric Equation
  10. 10The number of solutions of equation is03 Apr, 2025 (E)Solving Trigonometric Equation
  11. 11If , then the number of solutions of , is equal to:02 Apr, 2025 (M)Solving Trigonometric Equation
  12. 12If , then the number of solutions of , is equal to02 Apr, 2025 (E)Solving Trigonometric Equation
  13. 13The sum of all values of satisfying and is22 Jan, 2025 (E)Solving Trigonometric Equation
  14. 14Suppose is a solution of . Then is equal to :05 Apr, 2024 (M)Solving Trigonometric Equation
  15. 15The number of solutions of , where , is________05 Apr, 2024 (E)Solving Trigonometric Equation
  16. 16Let has real roots . If and be the smallest and largest elements of the set , respectively, then equals _________04 Apr, 2024 (E)Solving Trigonometric Equation
  17. 17The number of solutions of the equation 4 sin 2 x − 4 cos 3 x + 9 − 4 cos x = 0 ; x ∈ − 2 π , 2 π is:01 Feb, 2024 (E)Solving Trigonometric Equation
  18. 18If 2 sin 3 x + sin 2 x cos x + 4 sin x - 4 = 0 has exactly 3 solutions in the interval 0 , n π 2 , n ∈ N , then the roots of the equation x 30 Jan, 2024 (M)Solving Trigonometric Equation
  19. 19If α , - π 2 α π 2 is the solution of 4 cos θ + 5 sin θ = 1 , then the value of tan α is29 Jan, 2024 (M)Solving Trigonometric Equation
  20. 20The sum of the solutions x ∈ R of the equation 3 cos 2 x + cos 3 2 x cos 6 x - sin 6 x = x 3 - x 2 + 6 is29 Jan, 2024 (E)Solving Trigonometric Equation
  21. 21Let the set of all a ∈ R such that the equation cos 2 x + a sin x = 2 a - 7 has a solution be [ p , q ] and r = tan 9 ° - tan 27 ° - 1 cot 627 Jan, 2024 (M)Solving Trigonometric Equation
  22. 22If 2 tan 2 θ - 5 sec θ = 1 has exactly 7 solutions in the interval 0 , n π 2 , for the least value of n ∈ N then ∑ k = 1 n k 2 k is equal to27 Jan, 2024 (E)Solving Trigonometric Equation
  23. 23The number of elements in the set S = [ 0 , 2 ] : 3 cos 4 - 5 cos 2 - 2 sin 6 + 2 = 0 is11 Apr, 2023 (M)Solving Trigonometric Equation
  24. 24Let S = x - 2 , 2 : 9 1 - tan 2 x + 9 tan 2 x = 10 and = x S tan 2 x 3 , then 1 6 ( - 14 ) 2 is equal to10 Apr, 2023 (E)Solving Trigonometric Equation
  25. 25Let f ( ) = 3 sin 4 3 2 - + sin 4 ( 3 + ) - 2 1 - sin 2 2 and S = [ 0 , ] : f ( ) = - 3 2 . If 4 = S then f ( ) is equal to29 Jan, 2023 (M)Solving Trigonometric Equation
  26. 26The set of all values of for which the equation cos 2 2 x - 2 sin 4 x - 2 cos 2 x =29 Jan, 2023 (E)Solving Trigonometric Equation
  27. 27If m and n respectively are the numbers of positive and negative value of in the interval - , that satisfy the equation cos 2 cos 2 = cos 3 25 Jan, 2023 (E)Solving Trigonometric Equation
  28. 28Let S = [ 0 , 2 ) : tan cos + tan sin = 0 , then S sin 2 + 4 is equal to24 Jan, 2023 (E)Solving Trigonometric Equation
  29. 29Let S = ( 0 , 2 ) : 7 cos 2 - 3 sin 2 - 2 cos 2 2 = 2 . Then, the sum of roots of all the equations x 2 - 2 tan 2 + cot 2 x + 6 sin 2 = 0 S 29 Jul, 2022 (M)Solving Trigonometric Equation
  30. 30The number of elements in the set S = x : 2 cos x 2 + x 6 = 4 x + 4 - x is29 Jul, 2022 (E)Solving Trigonometric Equation
  31. 31Let S = - , 2 - - 2 , - 4 , - 3 4 , 4 . Then the number of elements in the set A = S : tan 1 + 5 tan 2 = 5 - tan 2 is _____ .28 Jul, 2022 (E)Solving Trigonometric Equation
  32. 32Let S = 0 , 2 : 8 2 sin 2 + 8 2 cos 2 = 16 . Then n S + S sec 4 + 2 cosec 4 + 2 is equal to:26 Jul, 2022 (M)Solving Trigonometric Equation
  33. 33If the sum of solutions of the system of equations 2 sin 2 - cos 2 = 0 and 2 cos 2 + 3 sin = 0 in the interval 0 , 2 is k , then k is equal 26 Jul, 2022 (E)Solving Trigonometric Equation
  34. 34The number of solutions of cos x = sin x , such that - 4 x 4 is25 Jul, 2022 (M)Solving Trigonometric Equation
  35. 35The number of elements in the set S = - 4 , 4 : 3 cos 2 2 + 6 cos 2 - 10 cos 2 + 5 = 0 is ______.29 Jun, 2022 (M)Solving Trigonometric Equation
  36. 36The number of solutions of the equation 2 - cos 2 + 2 = 0 in R is equal to ______.29 Jun, 2022 (M)Solving Trigonometric Equation
  37. 37The number of solutions of the equation sin x = cos 2 x in the interval 0 , 10 is ______.29 Jun, 2022 (E)Solving Trigonometric Equation
  38. 38The number of values of x in the interval 4 , 7 4 for which 14 cosec 2 x - 2 sin 2 x = 21 - 4 cos 2 x holds, is ______.25 Jun, 2022 (M)Solving Trigonometric Equation
  39. 39Let S = [ - , ] - 2 : sin tan + tan = sin 2 . If T = S cos 2 , then T + n S is equal to24 Jun, 2022 (M)Solving Trigonometric Equation
  40. 40The number of solutions of the equation cos x + 3 cos 3 - x = 1 4 cos 2 2 x , x - 3 , 3 is:24 Jun, 2022 (E)Solving Trigonometric Equation
  41. 41If n is the number of solutions of the equation 2 cos x 4 sin 4 + x sin 4 - x - 1 = 1 , x 0 , and S is the sum of all these solutions, then 01 Sep, 2021 (E)Solving Trigonometric Equation
  42. 42Let S be the sum of all solutions (in radians) of the equation sin 4 + cos 4 - sin cos = 0 in [ 0 , 4 ] then 8 S is equal to27 Aug, 2021 (E)Solving Trigonometric Equation
  43. 43The sum of solutions of the equation cos x 1 + sin x = tan 2 x , x - 2 , 2 - - 4 , 4 is:26 Aug, 2021 (M)Solving Trigonometric Equation
  44. 44The sum of all values of x in [ 0 , 2 ] , for which sin x + sin 2 x + sin 3 x + sin 4 x = 0 , is equal to :25 Jul, 2021 (M)Solving Trigonometric Equation
  45. 45The number of distinct real roots of sin x cos x cos x cos x sin x cos x cos x cos x sin x = 0 in the interval - 4 x 4 is:25 Jul, 2021 (E)Solving Trigonometric Equation
  46. 46The number of solutions of sin 7 x + cos 7 x = 1 , x [ 0 , 4 ] is equal to22 Jul, 2021 (M)Solving Trigonometric Equation
  47. 47The solutions of the equation 1 + sin 2 x sin 2 x sin 2 x cos 2 x 1 + cos 2 x cos 2 x 4 sin 2 x 4 sin 2 x 1 + 4 sin 2 x = 0 , 0 x , are18 Mar, 2021 (M)Solving Trigonometric Equation
  48. 48The number of solutions of the equation | cot x | = cot x + 1 sin x in the interval [ 0 , 2 ] is18 Mar, 2021 (M)Solving Trigonometric Equation
  49. 49The number of solutions of the equation x + 2 tan x = 2 in the interval 0 , 2 is17 Mar, 2021 (E)Solving Trigonometric Equation
  50. 50The number of roots of the equation, 81 sin 2 x + 81 cos 2 x = 30 in the interval 0 , is equal to :16 Mar, 2021 (M)Solving Trigonometric Equation

Frequently Asked Questions

1.How many questions are available for Trigonometric Equations?

This chapter includes 78 questions compiled from JEE Main papers spanning 2002 to 2026.

2.Are these questions only from JEE Main, or from other exams too?

These are JEE Main questions specifically for the Trigonometric Equations chapter. Questions from other exams like NTA Abhyas (JEE Main) or JEE Advanced are organised separately under their respective exam sections.

3.Is Trigonometric Equations an important chapter for JEE Main Mathematics?

Trigonometric Equations has appeared in 16 of the 25 years of JEE Main papers covered here, with 78 questions across 73 papers - about one per paper it appears in.

4.What is the difficulty level of Trigonometric Equations questions in JEE Main?

Of the 78 questions analysed for this chapter, 18% are easy, 59% moderate and 23% tough. 2021 had the most, with 13 questions.

5.Which topics in Trigonometric Equations should I focus on?

These topics have carried the most weightage in Trigonometric Equations:

  • Solving Trigonometric Equation - 75 questions (96%)
  • Solving Trigonometric Inequalities - 3 questions (4%)
  • Solving Trigonometric Equation has produced the most tough questions (18).
6.Is Trigonometric Equations's weightage in JEE Main going up or down?

Across all 73 papers analysed, Trigonometric Equations has averaged about 1.1 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.4 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.