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Mathematics - Inverse Trigonometric Functions

Practise 91 JEE Main previous year questions on Inverse Trigonometric Functions, 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.

Inverse Trigonometric Functions has been asked in 18 of the 25 years of JEE Main papers analysed (2002–2026), with 91 questions in all. 24% of them were easy, 56% moderate and 20% tough. Most of its questions came from 2021, with 14 questions that year. In the last three years (2024–2026) it had 23 questions across 49 papers, about 0.5 per paper.

The chapter's 8 topics are not weighted equally: Sum and difference of angles (27 questions, 30%), Principal Value and Basics (18 questions, 20%), and Converting one Inverse T function to other Inverse T (11 questions, 12%) have been asked the most. Sum and difference of angles has also led over the last five years, with 17 questions. Sum and difference of angles has produced the most tough questions (5).

  1. 1Let and , where inverse trigonometric functions take only the principal values. Given below are two statements: Statement I: . Statement II:08 Apr, 2026 (E)Principal Value and Basics
  2. 2Let denote the greatest integer function. If the domain of the function is , then is equal to:06 Apr, 2026 (M)Principal Value and Basics
  3. 3Let , and . Then is equal to:06 Apr, 2026 (M)Sum and difference of angles
  4. 4If , , then the value of is :06 Apr, 2026 (E)Converting one Inverse T function to other Inverse T
  5. 5If , then is equal to __________.05 Apr, 2026 (M)Sum and difference of angles
  6. 6If , then at is equal to:04 Apr, 2026 (M)T inverse T property
  7. 7If , then the number of solutions of the equation is28 Jan, 2026 (M)Sum and difference of angles
  8. 8Considering the principal values of inverse trigonometric functions, the value of the expression is equal to :28 Jan, 2026 (E)Multiple Angles
  9. 9If the domain of the function , is , then is equal to24 Jan, 2026 (E)Principal Value and Basics
  10. 10The number of solutions of , where , is equal to22 Jan, 2026 (M)Sum and difference of angles
  11. 11If the domain of the function is the interval , then is equal to :21 Jan, 2026 (M)Principal Value and Basics
  12. 12Let the maximum value of for be , where . Then is equal to .21 Jan, 2026 (E)Sum of complementary angles
  13. 13The value of08 Apr, 2025 (E)Converting one Inverse T function to other Inverse T
  14. 14Considering the principal values of the inverse trigonometric functions, , is equal to04 Apr, 2025 (M)Sum and difference of angles
  15. 15The sum of the infinite series is :-04 Apr, 2025 (E)Infinite Series
  16. 16If , then is equal to _____.02 Apr, 2025 (E)Sum and difference of angles
  17. 17Let \( {S}= \{x: ^{-1} x= + ^{-1} x+ ^{-1}(2 x+1) \}\). Then \( _{x {~S}}(2 x-1)^2\) is equal to ______.29 Jan, 2025 (M)Sum and difference of angles
  18. 18is equal to:28 Jan, 2025 (M)Sum and difference of angles
  19. 19If for some and , then is_______.24 Jan, 2025 (M)Principal Value and Basics
  20. 20If , then the expression is equal to :24 Jan, 2025 (E)Sum and difference of angles
  21. 21Using the principal values of the inverse trigonometric functions, the sum of the maximum and the minimum values of is :22 Jan, 2025 (M)T inverse T property
  22. 22The integral is equal to09 Apr, 2024 (E)Converting one Inverse T function to other Inverse T
  23. 23Let the inverse trigonometric functions take principal values. The number of real solutions of the equation , is _______09 Apr, 2024 (E)Converting one Inverse T function to other Inverse T
  24. 24For , if , then is equal to_____06 Apr, 2024 (M)T inverse T property
  25. 25Given that the inverse trigonometric function assumes principal values only. Let , be any two real numbers in such that . Then, the minimum 04 Apr, 2024 (E)Principal Value and Basics
  26. 26For α , β , γ ≠ 0 . If sin − 1 α + sin − 1 β + sin − 1 γ = π and α + β + γ α − γ + β = 3 α β , then γ equal to31 Jan, 2024 (M)Sum and difference of angles
  27. 27If a = sin − 1 sin 5 and b = cos − 1 cos 5 , then a 2 + b 2 is equal to31 Jan, 2024 (E)Principal Value and Basics
  28. 28Let x = m n ( m , n are co-prime natural numbers) be a solution of the equation cos 2 sin - 1 x = 1 9 and let α , β ( α β ) be the roots of 29 Jan, 2024 (E)Multiple Angles
  29. 29Considering only the principal values of inverse trigonometric functions, the number of positive real values of x satisfying tan - 1 ( x ) +27 Jan, 2024 (E)Sum and difference of angles
  30. 30If S = x : sin - 1 x + 1 x 2 + 2 x + 2 - sin - 1 x x 2 + 1 = 4 then x S sin x 2 + x + 5 2 - cos x 2 + x + 5 is equal to _ _ _ _ _ _ _ _ _ .13 Apr, 2023 (M)Sum and difference of angles
  31. 31For x ( - 1 , 1 ] , the number of solutions of the equation sin - 1 x = 2 tan - 1 x is equal to13 Apr, 2023 (E)Multiple Angles
  32. 32Let S be the set of all solutions of the equation cos - 1 2 x - 2 cos - 1 1 - x 2 = , x - 1 2 , 1 2 . Then x S 2 sin - 1 x 2 - 1 is equal to01 Feb, 2023 (M)Sum and difference of angles
  33. 33Let S = x R : 0 x 1 and 2 tan - 1 1 - x 1 + x = cos - 1 1 - x 2 1 + x 2 . If n ( S ) denotes the number of elements in S then :01 Feb, 2023 (E)Converting one Inverse T function to other Inverse T
  34. 34If sin - 1 17 + cos - 1 4 5 - tan - 1 77 36 = 0 , 0 13 , then sin - 1 sin + cos - 1 cos is equal to31 Jan, 2023 (M)Sum and difference of angles
  35. 35Let y = f x represent a parabola with focus - 1 2 , 0 and directrix y = - 1 2 . Then S = x : tan - 1 f x + sin - 1 f x + 1 = 2 :31 Jan, 2023 (M)Sum and difference of angles
  36. 36Let a , b 0 , 2 be the largest interval for which sin - 1 sin - cos - 1 sin 0 , 0 , 2 , holds . If x 2 + x + sin - 1 x 2 - 6 x + 10 + cos - 31 Jan, 2023 (E)T inverse T property
  37. 37Let a 1 = 1 , a 2 , a 3 , a 4 , . . be consecutive natural numbers. Then tan - 1 1 1 + a 1 a 2 + tan - 1 1 1 + a 2 a 3 + . . + tan - 1 1 1 +30 Jan, 2023 (E)Infinite Series
  38. 38If the sum of all the solutions of tan - 1 2 x 1 - x 2 + cot - 1 1 - x 2 2 x = 3 , - 1 x 1 , x 0 , is - 4 3 , then is equal to _____ .25 Jan, 2023 (M)Multiple Angles
  39. 39tan - 1 1 + 3 3 + 3 + sec - 1 8 + 4 3 6 + 3 3 =24 Jan, 2023 (M)Converting one Inverse T function to other Inverse T
  40. 40Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation cos - 1 x - 2 sin - 1 28 Jul, 2022 (M)Sum and difference of angles
  41. 41For k , let the solutions of the equation cos sin - 1 x cot tan - 1 cos sin - 1 x = k , 0 x 1 2 be and , where the inverse trigonometric fun27 Jul, 2022 (M)Converting one Inverse T function to other Inverse T
  42. 42tan 2 tan - 1 1 5 + sec - 1 5 2 + 2 tan - 1 1 8 is equal to:26 Jul, 2022 (M)Sum and difference of angles
  43. 43If 0 x 1 2 and sin - 1 x = cos - 1 x , then a value of sin 2 + is26 Jul, 2022 (E)Sum of complementary angles
  44. 44Let x = sin 2 tan - 1 and y = sin 1 2 tan - 1 4 3 . If S = : y 2 = 1 - x , then S 16 3 is equal to _______.25 Jul, 2022 (E)Multiple Angles
  45. 4550 tan 3 tan - 1 1 2 + 2 cos - 1 1 5 + 4 2 tan 1 2 tan - 1 2 2 is equal to ______.29 Jun, 2022 (M)Multiple Angles
  46. 46The value of lim n 6 tan r = 1 n tan - 1 1 r 2 + 3 r + 3 is equal to28 Jun, 2022 (E)Infinite Series
  47. 47sin - 1 sin 2 3 + cos - 1 cos 7 6 + tan - 1 tan 3 4 is equal to27 Jun, 2022 (M)T inverse T property
  48. 48The value of cot n = 1 50 tan - 1 1 1 + n + n 2 is27 Jun, 2022 (E)Infinite Series
  49. 49If the inverse trigonometric functions take principal values, then cos - 1 3 10 cos tan - 1 4 3 + 2 5 sin tan - 1 4 3 is equal to26 Jun, 2022 (E)T inverse T property
  50. 50The value of tan - 1 cos 15 4 - 1 sin 4 is equal to25 Jun, 2022 (E)Principal Value and Basics

Frequently Asked Questions

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

This chapter includes 91 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 Inverse Trigonometric Functions chapter. Questions from other exams like NTA Abhyas (JEE Main) or JEE Advanced are organised separately under their respective exam sections.

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

Inverse Trigonometric Functions has appeared in 18 of the 25 years of JEE Main papers covered here, with 91 questions across 87 papers - about one per paper it appears in.

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

Of the 91 questions analysed for this chapter, 24% are easy, 56% moderate and 20% tough. 2021 had the most, with 14 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 - 27 questions (30%)
  • Principal Value and Basics - 18 questions (20%)
  • Converting one Inverse T function to other Inverse T - 11 questions (12%)
  • Sum and difference of angles has produced the most tough questions (5).
6.Is Inverse Trigonometric Functions's weightage in JEE Main going up or down?

Across all 87 papers analysed, Inverse Trigonometric Functions has averaged about 1.0 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.5 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.