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Mathematics - Trigonometric Ratios & Identities

Practise 295 NDA previous year questions on Trigonometric Ratios & Identities, compiled from papers spanning 2010 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 NDA tests.

Trigonometric Ratios & Identities has been asked in 17 of the 21 years of NDA papers analysed (2006–2026), with 295 questions in all. 27% of them were easy, 70% moderate and 2% tough. Most of its questions came from 2019, with 31 questions that year. In the last three years (2024–2026) it had 38 questions across 5 papers, about 7.6 per paper.

The chapter's 7 topics are not weighted equally: Basic Identities & T Ratios (120 questions, 41%), Sum and Difference & Multiple angle Formula (118 questions, 40%), and Maximum and Minimum Values (23 questions, 8%) have been asked the most. Over the last five years the most frequent topics have been Sum and Difference & Multiple angle Formula (38), Basic Identities & T Ratios (24), and Maximum and Minimum Values (4). Sum and Difference & Multiple angle Formula has produced the most tough questions (5).

  1. 1If , then which one of the following is a possible value of ?2026 (Phase 1)Sum and Difference & Multiple angle Formula
  2. 2If and are complementary angles such that and , then what is equal to ?2026 (Phase 1)Measurement of Angles
  3. 3If and , then which one of the following is correct ?2026 (Phase 1)Basic Identities & T Ratios
  4. 4If , then what is the value of ?2026 (Phase 1)Transformation Formulas
  5. 5is maximum when is equal to2026 (Phase 1)Maximum and Minimum Values
  6. 6If lies in the fourth quadrant and , then what is the value of ?2026 (Phase 1)Basic Identities & T Ratios
  7. 7If , then what is a value of ?2026 (Phase 1)Sum and Difference & Multiple angle Formula
  8. 8In a triangle , then what is equal to ?2026 (Phase 1)Sum and Difference & Multiple angle Formula
  9. 9If and are acute angles such that , then what is the maximum value of ?2026 (Phase 1)Sum and Difference & Multiple angle Formula
  10. 10Consider the following for the three (03) items that follow: Let , and . What is equal to?2025 (Phase 1)Basic Identities & T Ratios
  11. 11Consider the following for the three (03) items that follow: Let , and . What is equal to?2025 (Phase 1)Transformation Formulas
  12. 12Consider the following for the three (03) items that follow: Let , and . What is equal to?2025 (Phase 1)Basic Identities & T Ratios
  13. 13Consider the following for the two (02) items that follow: Let . What is the minimum value of ?2025 (Phase 1)Sum and Difference & Multiple angle Formula
  14. 14Consider the following for the two (02) items that follow: Let . What is the maximum value of ?2025 (Phase 1)Sum and Difference & Multiple angle Formula
  15. 15Consider the following for the three (03) items that follow: Let and . What is equal to?2025 (Phase 1)Basic Identities & T Ratios
  16. 16Consider the following for the three (03) items that follow: Let and . What is equal to?2025 (Phase 1)Sum and Difference & Multiple angle Formula
  17. 17Consider the following for the three (03) items that follow: Let and . What is equal to?2025 (Phase 1)Sum and Difference & Multiple angle Formula
  18. 18Consider the following for the two (02) items that follow: Let , where $ equal to?2025 (Phase 1)Basic Identities & T Ratios
  19. 19Consider the following for the two (02) items that follow: Let , where 2 2 + 2 $ equal to?2025 (Phase 1)Sum and Difference & Multiple angle Formula
  20. 20For the following two (02) items: Let and . What is equal to?2025 (Phase 2)Transformation Formulas
  21. 21For the following two (02) items: Let and . What is equal to?2025 (Phase 2)Transformation Formulas
  22. 22For the following two (02) items: Let and . What is equal to?2025 (Phase 2)Sum and Difference & Multiple angle Formula
  23. 23For the following two (02) items: Let and . What is equal to?2025 (Phase 2)Basic Identities & T Ratios
  24. 24If is a triangle, then what is the value of the determinant ?2024 (Phase 1)Basic Identities & T Ratios
  25. 25What is equal to?2024 (Phase 1)Sum and Difference & Multiple angle Formula
  26. 26What is equal to?2024 (Phase 1)Basic Identities & T Ratios
  27. 27ABC is a triangle such that angle , then what is equal to?2024 (Phase 1)Sum and Difference & Multiple angle Formula
  28. 28What is the value of . equal to?2024 (Phase 1)Sum and Difference & Multiple angle Formula
  29. 29If and , then what is the value of ?2024 (Phase 1)Basic Identities & T Ratios
  30. 30If and are the roots of the equation , then what is the value of2024 (Phase 1)Sum and Difference & Multiple angle Formula
  31. 31What is the value of2024 (Phase 1)Sum and Difference & Multiple angle Formula
  32. 32In a triangle What is the value of ?2024 (Phase 2)Sum of three of more angles
  33. 33What is equal to?2024 (Phase 2)Sum and Difference & Multiple angle Formula
  34. 34What is equal to?2024 (Phase 2)Sum and Difference & Multiple angle Formula
  35. 35Consider the following numbers: A. B. C. How many of the above are irrational numbers?2024 (Phase 2)Basic Identities & T Ratios
  36. 36If then what is equal to?2024 (Phase 2)Sum and Difference & Multiple angle Formula
  37. 37If , then what is equal to? equal to?2024 (Phase 2)Sum and Difference & Multiple angle Formula
  38. 38What is the maximum value of the ?2024 (Phase 2)Maximum and Minimum Values
  39. 39Paragraph: Let be the GM of and be the AM of and Question: What is equal to?2023 (Phase 1)Basic Identities & T Ratios
  40. 40Paragraph: Let be the GM of and be the AM of and Question: What is the value of of ?2023 (Phase 1)Sum and Difference & Multiple angle Formula
  41. 41Paragraph: Given that Question: The given equation can be reduced to2023 (Phase 1)Basic Identities & T Ratios
  42. 42Paragraph: Given that Question: If , where a and b are natural numbers and c is prime number, then what is the value of ?2023 (Phase 1)Sum and Difference & Multiple angle Formula
  43. 43Paragraph: Let where [.] is a greatest integer function. Question: What is equal to?2023 (Phase 1)Basic Identities & T Ratios
  44. 44Paragraph: Let where [.] is a greatest integer function. Question: What is equal to?2023 (Phase 1)Basic Identities & T Ratios
  45. 45If , then what is equal to?2023 (Phase 1)Sum and Difference & Multiple angle Formula
  46. 46If then what is the value of ?2023 (Phase 2)Sum and Difference & Multiple angle Formula
  47. 47A function is defined by What is the period of the function?2023 (Phase 2)Basic Identities & T Ratios
  48. 48Let and . What is the value of ?2023 (Phase 2)Sum and Difference & Multiple angle Formula
  49. 49Let and . What is the value of ?2023 (Phase 2)Sum and Difference & Multiple angle Formula
  50. 50Let and . What is pq equal to2023 (Phase 2)Sum and Difference & Multiple angle Formula

Frequently Asked Questions

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

This chapter includes 295 questions compiled from NDA papers spanning 2010 to 2026.

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

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

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

Trigonometric Ratios & Identities has appeared in 17 of the 17 years of NDA papers covered here, with 295 questions across 32 papers - about 9 per paper it appears in.

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

Of the 295 questions analysed for this chapter, 27% are easy, 70% moderate and 2% tough. 2019 had the most, with 31 questions.

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

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

  • Basic Identities & T Ratios - 120 questions (41%)
  • Sum and Difference & Multiple angle Formula - 118 questions (40%)
  • Maximum and Minimum Values - 23 questions (8%)
  • Sum and Difference & Multiple angle Formula has produced the most tough questions (5).
6.Is Trigonometric Ratios & Identities's weightage in NDA going up or down?

Across all 32 papers analysed, Trigonometric Ratios & Identities has averaged about 9.2 questions per paper. In the last three years (2024–2026), that average has fallen, at about 7.6 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.