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Mathematics - Trigonometric Ratios & Identities

Practise 66 JEE Main previous year questions on Trigonometric Ratios & Identities, 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 Ratios & Identities has been asked in 17 of the 25 years of JEE Main papers analysed (2002–2026), with 66 questions in all. 35% of them were easy, 52% moderate and 14% tough. Most of its questions came from 2026, with 9 questions that year. In the last three years (2024–2026) it had 18 questions across 49 papers, about 0.4 per paper.

The chapter's 7 topics are not weighted equally: Sum and Difference & Multiple angle Formula (27 questions, 41%), Basic Identities & T Ratios (13 questions, 20%), and Transformation Formulas (12 questions, 18%) have been asked the most. Sum and Difference & Multiple angle Formula has also led over the last five years, with 16 questions. Sum and Difference & Multiple angle Formula has produced the most tough questions (7).

  1. 1If and , then is equal to _____.04 Apr, 2026 (M)Sum and Difference & Multiple angle Formula
  2. 2If , then the value of is :02 Apr, 2026 (M)Sum and Difference & Multiple angle Formula
  3. 3Let and . Then is:02 Apr, 2026 (E)Sum and Difference & Multiple angle Formula
  4. 4If , then28 Jan, 2026 (M)Sum and Difference & Multiple angle Formula
  5. 5If for some , then is equal to24 Jan, 2026 (M)Sum and Difference & Multiple angle Formula
  6. 6The value of is equal to24 Jan, 2026 (M)Sum and Difference & Multiple angle Formula
  7. 7Let and respectively be the maximum and the minimum values of the function . Then is equal to :23 Jan, 2026 (M)Maximum and Minimum Values
  8. 8The least value of is23 Jan, 2026 (E)Maximum and Minimum Values
  9. 9Let ( {15 }{2} )( 8 + 8 )+ ( {15 }{2} )( 8 - 8 )$ is equal to23 Jan, 2026 (E)Sum and Difference & Multiple angle Formula
  10. 10If , where , then is equal to22 Jan, 2026 (M)Sum and Difference & Multiple angle Formula
  11. 11Let and , where and . If , then is equal to .22 Jan, 2026 (E)Sum and Difference & Multiple angle Formula
  12. 12The value of is equal to :21 Jan, 2026 (M)Sum and Difference & Multiple angle Formula
  13. 13If , then is equal to :29 Jan, 2025 (E)Basic Identities & T Ratios
  14. 14If , then is equal to :28 Jan, 2025 (E)Sum and Difference & Multiple angle Formula
  15. 15The value of is23 Jan, 2025 (M)Transformation Formulas
  16. 16If , then is equal to23 Jan, 2025 (M)Transformation Formulas
  17. 17Let . Then, the sum of all , where attains its maximum value, is :09 Apr, 2024 (M)T-Ratios of Multiple & sub multiple angles
  18. 18If , where , then is equal to08 Apr, 2024 (M)Basic Identities & T Ratios
  19. 19If the value of is , where are natural numbers and , then is equal to :08 Apr, 2024 (E)T-Ratios of Multiple & sub multiple angles
  20. 20If tan A = 1 x x 2 + x + 1 , tan B = x x 2 + x + 1 and tan C = x − 3 + x − 2 + x − 1 1 2 , 0 A , B , C π 2 , then A + B is equal to:01 Feb, 2024 (M)Sum and Difference & Multiple angle Formula
  21. 21For α , β ∈ 0 , π 2 let 3 sin ( α + β ) = 2 sin ( α - β ) and a real number k be such that tan α = tan β . Then the value of k is equal to30 Jan, 2024 (E)Sum and Difference & Multiple angle Formula
  22. 2296 cos 33 cos 2 33 cos 4 33 cos 8 33 cos 16 33 is equal to10 Apr, 2023 (M)Trigonometric Series
  23. 23The value of 36 4 cos 2 9 - 1 4 cos 2 27 - 1 4 cos 2 81 - 1 4 cos 2 243 - 1 is08 Apr, 2023 (E)Transformation Formulas
  24. 24The value of tan 9 o - tan 27 o - tan 63 o + tan 81 o is _____.06 Apr, 2023 (E)Basic Identities & T Ratios
  25. 25If tan 15 + 1 tan 75 + 1 tan 105 + tan 195 = 2 a , then the value of a + 1 a is :30 Jan, 2023 (M)Basic Identities & T Ratios
  26. 26Let S = 0 , 2 : m = 1 9 sec + m - 1 6 sec + m 6 = - 8 3 . Then27 Jul, 2022 (E)Sum and Difference & Multiple angle Formula
  27. 27The value of 2 sin 22 sin 3 22 sin 5 22 sin 7 22 sin 9 22 is equal to:25 Jul, 2022 (E)Transformation Formulas
  28. 28If cot = 1 and sec = - 5 3 , where 3 2 and 2 , then the value of tan + and the quadrant in which + lies, respectively are28 Jun, 2022 (E)Sum and Difference & Multiple angle Formula
  29. 29The value of cos 2 7 + cos 4 7 + cos 6 7 is equal to27 Jun, 2022 (M)Transformation Formulas
  30. 30= sin 36 is a root of which of the following equation27 Jun, 2022 (E)T-Ratios of Multiple & sub multiple angles
  31. 31If sin 2 10 sin 20 sin 40 sin 50 sin 70 = - 1 16 sin 10 , then 16 + - 1 is equal to _____.26 Jun, 2022 (M)Transformation Formulas
  32. 3216 sin 20 sin 40 sin 80 is equal to26 Jun, 2022 (E)Sum and Difference & Multiple angle Formula
  33. 33The value of 2 sin 12 - sin 72 is25 Jun, 2022 (E)Transformation Formulas
  34. 34cosec 18 is a root of the equation:31 Aug, 2021 (M)Sum and Difference & Multiple angle Formula
  35. 35A 10 inches long pencil A B with mid point C and a small eraser P are placed on the horizontal top of a table such that P C = 5 inches and P26 Aug, 2021 (E)Sum and Difference & Multiple angle Formula
  36. 36The value of 2 sin 8 sin 2 8 sin 3 8 sin 5 8 sin 6 8 sin 7 8 is :26 Aug, 2021 (E)Transformation Formulas
  37. 37If sin + cos = 1 2 , then 16 sin 2 + cos 4 + sin 6 is equal to:27 Jul, 2021 (M)Sum and Difference & Multiple angle Formula
  38. 38The value of cot 24 is:25 Jul, 2021 (E)Sum and Difference & Multiple angle Formula
  39. 39If 15 sin 4 + 10 cos 4 = 6 , for some R , then the value of 27 sec 6 + 8 cosec 6 is equal to :18 Mar, 2021 (E)Basic Identities & T Ratios
  40. 40The number of integral values of k for which the equation 3 sin x + 4 cos x = k + 1 has a solution, k R is _______.26 Feb, 2021 (M)Maximum and Minimum Values
  41. 41If L = sin 2 16 - sin 2 8 and M = cos 2 16 - sin 2 805 Sep, 2020 (E)Sum and Difference & Multiple angle Formula
  42. 42If the equation cos 4 + sin 4 + = 0 has real solutions for then lies in interval02 Sep, 2020 (E)Maximum and Minimum Values
  43. 43The value of cos 3 8 . cos 3 8 + sin 3 8 . sin 3 8 is:09 Jan, 2020 (M)Sum and Difference & Multiple angle Formula
  44. 44If 2 s i n 1 + c o s 2 = 1 7 and 1 - c o s 2 2 = 1 10 , , 0 , 2 , then t a n + 2 , is equal to08 Jan, 2020 (E)Sum and Difference & Multiple angle Formula
  45. 45The equation y = s i n x sin x + 2 - sin 2 ( x + 1 ) represents a straight line lying in:12 Apr, 2019 (M)Transformation Formulas
  46. 46The value of cos 2 10 cos 10 cos 50 + c o s 2 50 is09 Apr, 2019 (M)Transformation Formulas
  47. 47The value of s i n 10 s i n 30 s i n 50 s i n 70 is:09 Apr, 2019 (E)Sum and Difference & Multiple angle Formula
  48. 48If c o s + = 3 5 , sin ( - ) = 5 13 and 0 , 4 , then tan 2 is equal to:08 Apr, 2019 (M)Sum and Difference & Multiple angle Formula
  49. 49The maximum value of 3 cos + 5 sin - 6 for any real value of is :12 Jan, 2019 (M)Maximum and Minimum Values
  50. 50Let for Then for all the value of is equal to :11 Jan, 2019 (M)Basic Identities & T Ratios

Frequently Asked Questions

1.How many questions are available for Trigonometric Ratios & Identities?

This chapter includes 66 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 Ratios & Identities chapter. Questions from other exams like NTA Abhyas (JEE Main) or JEE Advanced are organised separately under their respective exam sections.

3.Is Trigonometric Ratios & Identities an important chapter for JEE Main Mathematics?

Trigonometric Ratios & Identities has appeared in 17 of the 25 years of JEE Main papers covered here, with 66 questions across 61 papers - about one per paper it appears in.

4.What is the difficulty level of Trigonometric Ratios & Identities questions in JEE Main?

Of the 66 questions analysed for this chapter, 35% are easy, 52% moderate and 14% tough. 2026 had the most, with 9 questions.

5.Which topics in Trigonometric Ratios & Identities should I focus on?

These topics have carried the most weightage in Trigonometric Ratios & Identities:

  • Sum and Difference & Multiple angle Formula - 27 questions (41%)
  • Basic Identities & T Ratios - 13 questions (20%)
  • Transformation Formulas - 12 questions (18%)
  • Sum and Difference & Multiple angle Formula has produced the most tough questions (7).
6.Is Trigonometric Ratios & Identities's weightage in JEE Main going up or down?

Across all 61 papers analysed, Trigonometric Ratios & Identities 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.