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Mathematics - Inverse Trigonometric Functions

Practise 67 NDA previous year questions on Inverse Trigonometric Functions, 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.

Inverse Trigonometric Functions has been asked in 17 of the 21 years of NDA papers analysed (2006–2026), with 67 questions in all. 27% of them were easy, 73% moderate and 0% tough. Most of its questions came from 2015, with 7 questions that year. In the last three years (2024–2026) it had 12 questions across 5 papers, about 2.4 per paper.

The chapter's 6 topics are not weighted equally: Sum and difference of angles (29 questions, 43%), T inverse T property (24 questions, 36%), and Principal Value and Basics (8 questions, 12%) have been asked the most. Over the last five years the most frequent topics have been T inverse T property (7), Sum and difference of angles (6), and Multiple Angles (2).

  1. 1Consider the following in respect of inverse circular functions : I. II. III. IV. How many of the above are correct ?2026 (Phase 1)Negative and reciprocal Properties
  2. 2What is equal to ?2026 (Phase 1)Multiple Angles
  3. 3If is a root of , then what is equal to?2025 (Phase 1)Negative and reciprocal Properties
  4. 4If , then what is the value of ?2025 (Phase 1)Sum and difference of angles
  5. 5Consider the following for the two (02) items that follow: Let . What is equal to?2025 (Phase 1)Multiple Angles
  6. 6What is equal to?2025 (Phase 2)Sum and difference of angles
  7. 7What is the value of ?2025 (Phase 2)Principal Value and Basics
  8. 8If , then which one of the following is correct?2024 (Phase 1)T inverse T property
  9. 9What is equal to?2024 (Phase 1)T inverse T property
  10. 10What is equal to?2024 (Phase 1)Sum and difference of angles
  11. 11If , then what is equal to?2024 (Phase 2)Sum and difference of angles
  12. 12What is equal to?2024 (Phase 2)T inverse T property
  13. 13What is equal to?2023 (Phase 2)T inverse T property
  14. 14If , where ; then what is the value of ?2023 (Phase 2)T inverse T property
  15. 15What is equal to?2023 (Phase 2)T inverse T property
  16. 16If , where , then what is equal to?2022 (Phase 1)Sum and difference of angles
  17. 17If , then what is equal to?2022 (Phase 1)Sum and difference of angles
  18. 18What is equal to?2022 (Phase 2)T inverse T property
  19. 19The equation has2021 (Phase 1)Sum and difference of angles
  20. 20holds, when2021 (Phase 1)T inverse T property
  21. 21What is the value of the following?2021 (Phase 2)Sum and difference of angles
  22. 22Let for . What is the value of ?2021 (Phase 2)Principal Value and Basics
  23. 23What is the slope of the tangent of at2021 (Phase 2)T inverse T property
  24. 24What is the domain of the function ?2020Principal Value and Basics
  25. 25What is the value of ?2019 (Phase 1)T inverse T property
  26. 26If , then what is equal to ?2019 (Phase 1)Sum and difference of angles
  27. 27What is equal to?2019 (Phase 2)Multiple Angles
  28. 28What is the principal value of ?2018 (Phase 1)Principal Value and Basics
  29. 29What is equal to?2018 (Phase 1)Sum and difference of angles
  30. 30Consider the following values of x : 1. 8 2. -4 3. 4. Which of the above values of is/are the solutions of the equation2018 (Phase 2)Sum and difference of angles
  31. 31Let the slope of the curve be : Then the value of in the interval is2018 (Phase 2)T inverse T property
  32. 32Let be positive real numbers such that are in GP and and are in AP. Then which one of the following is correct?2017 (Phase 1)Sum and difference of angles
  33. 33The value of is equal to2017 (Phase 2)Sum and difference of angles
  34. 34The principal value of lies in the interval2017 (Phase 2)Principal Value and Basics
  35. 35If , then is equal to2017 (Phase 2)T inverse T property
  36. 36If , then is equal to2017 (Phase 2)T inverse T property
  37. 37Consider the following statements: 1. There exists for which . 2. Which of the above statements is/are correct?2016 (Phase 1)T inverse T property
  38. 38Consider the following statements: 1. 2. There exist , where such that Which of the above statements is/are correct?2016 (Phase 1)T inverse T property
  39. 39What is the value of ?2016 (Phase 2)T inverse T property
  40. 40The equation is satisfied by2015 (Phase 1)Sum and difference of angles
  41. 41Consider and What is equal to?2015 (Phase 1)Sum and difference of angles
  42. 42Consider and What is equal to?2015 (Phase 1)Sum and difference of angles
  43. 43Consider and What is equal to?2015 (Phase 1)Sum and difference of angles
  44. 44The value of is2015 (Phase 2)Sum and difference of angles
  45. 45Consider the following : 1. 2. which of the above is/are correct?2015 (Phase 2)Sum and difference of angles
  46. 46If , where , then is equal to2015 (Phase 2)T inverse T property
  47. 47If and are positive and , then what is equal to?2014 (Phase 1)Sum and difference of angles
  48. 48Consider the following statements: 1. 2. Which of the above statements is/are correct?2014 (Phase 1)Sum of complementary angles
  49. 49What is equal to?2014 (Phase 1)T inverse T property
  50. 50What is equal to?2014 (Phase 2)Sum and difference of angles

Frequently Asked Questions

1.How many questions are available for Inverse Trigonometric Functions?

This chapter includes 67 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 Inverse Trigonometric Functions chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Inverse Trigonometric Functions an important chapter for NDA Mathematics?

Inverse Trigonometric Functions has appeared in 17 of the 17 years of NDA papers covered here, with 67 questions across 31 papers - about 2 per paper it appears in.

4.What is the difficulty level of Inverse Trigonometric Functions questions in NDA?

Of the 67 questions analysed for this chapter, 27% are easy, 73% moderate and 0% tough. 2015 had the most, with 7 questions.

5.Which topics in Inverse Trigonometric Functions should I focus on?

These topics have carried the most weightage in Inverse Trigonometric Functions:

  • Sum and difference of angles - 29 questions (43%)
  • T inverse T property - 24 questions (36%)
  • Principal Value and Basics - 8 questions (12%)
6.Is Inverse Trigonometric Functions's weightage in NDA going up or down?

Across all 31 papers analysed, Inverse Trigonometric Functions has averaged about 2.2 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 2.4 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.