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Mathematics - Inverse Trigonometric Functions

Practise 71 NTA Abhyas (JEE Main) questions on Inverse Trigonometric Functions. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Inverse Trigonometric Functions has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 71 questions in all. 100% of them were easy, 0% moderate and 0% tough. Most of its questions came from 2025, with 0 questions that year. In the last three years (2023–2025) it had 0 questions across 63 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Uncategorized.

  1. 1The value of a for which a x 2 + sin - 1 x 2 - 2 x + 2 + cos - 1 x 2 - 2 x + 2 = 0 has a real solution, is
  2. 2If α = sin - 1 ⁡ 3 2 + sin - 1 ⁡ 1 3 and β = cos - 1 ⁡ 3 2 + cos - 1 ⁡ 1 3 , then
  3. 3The value of s i n c o t - 1 c o s c o t - 1 1 x is equal to x 0
  4. 4If s i n - 1 x 2 - 2 s i n - 1 x + 1 ≤ 0 (where, . represents the greatest integral part of x ), then
  5. 5If = c o t - 1 , = c o t - 1 and = - 1 , then the value of - is equal to
  6. 6The value of x for which sin ⁡ cot - 1 ⁡ 1 + x = cos ⁡ ( tan - 1 ⁡ x ) is
  7. 7Consider the function f x = c o s - 1 2 x + s i n - 1 2 x - 1 , then (where [.] represents the greatest integer part function)
  8. 8If f x = c o s - 1 x 3 2 - 1 - x - x 2 + x 3 , ∀ 0 ≤ x ≤ 1 , then the minimum value of f x is
  9. 9If 3 t a n - 1 1 2 + 3 - t a n - 1 1 3 = t a n - 1 1 x , then the value of x is equal to
  10. 10The value of 2 sin - 1 ⁡ 4 5 + 2 sin - 1 ⁡ 5 13 + 2 sin - 1 ⁡ 16 65 is equal to
  11. 11If a 1 , a 2 , a 3 are in arithmetic progression and d is the common difference, then tan - 1 ⁡ d 1 + a 1 a 2 + tan - 1 ⁡ d 1 + a 2 a 3 =
  12. 12If the value of the expression tan ⁡ 1 2 cos - 1 ⁡ 2 5 is in the form of a + b where a , b ∈ Z , then the value of a + b b is
  13. 13The number of solutions of the equation s i n - 1 x = sin ⁡ x - 1 is/are
  14. 14If f x = t a n - 1 x 2 + 4 x + s i n - 1 x 2 + 4 x + 1 , then
  15. 15If t a n - 1 1 2 x + 1 + t a n - 1 1 4 x + 1 = c o t - 1 x 2 2 , then the number of all possible values of x is/are
  16. 16If sin - 1 ⁡ 1 3 + sin - 1 ⁡ 2 3 = sin - 1 ⁡ x , then the value of x is
  17. 17The value of 2 cos - 1 ⁡ 2 3 - 2 cos - 1 ⁡ 6 + 1 2 3 is equal to
  18. 18The number of roots of the equation s i n - 1 x - c o s - 1 x = s i n - 1 5 x - 3 is/are
  19. 19If the maximum value of x which satisfies the inequality sin - 1 ⁡ sin ⁡ x ≥ cos - 1 ⁡ sin ⁡ x for x ∈ π 2 , 2 π is λ , then 2 λ 3 is equal
  20. 20The natural domain of the function f x = sin - 1 ⁡ 2 x + π 3 is
  21. 21If f x = t a n - 1 ln e 2 / x 3 ln e 2 x 3 + t a n - 1 ln e 2 x 3 ln e / x 6 x e , then the incorrect statement is
  22. 22If c o s - 1 sin x s i n - 1 sin x , then the number of integral values of x in the interval x 0,3 are
  23. 23If tan - 1 x 6 , then the maximum value of 3 x is (Use = 3 . 14 )
  24. 24If x satisfies the inequality t a n - 1 x 2 + 3 t a n - 1 x - 4 0 , then the complete set of values of x is
  25. 25The value(s) of x satisfying the equation sin - 1 ⁡ 1 - x - 2 sin - 1 ⁡ x = π 2 is/are
  26. 26If cos - 1 ⁡ x - x 2 2 + x 3 4 - … + sin - 1 ⁡ x 2 - x 4 2 + x 6 4 - … = π 2 for 0 x 2 , then x is equal to
  27. 27The value of sin - 1 ⁡ cos ⁡ sin - 1 ⁡ x + cos - 1 ⁡ sin ⁡ cos - 1 ⁡ x is equal to
  28. 28If the function f : R A defined as f x = tan - 1 2 x 3 1 + x 6 is a surjective function, then the set A is equal to
  29. 29The real solutions of the equation tan -1 x x + 1 + sin -1 x 2 + x + 1 = π 2 are
  30. 30If s i n - 1 5 x + s i n - 1 12 x = s i n - 1 2 x + c o s - 1 2 x , then the value of x is equal to
  31. 31If x , y , z are in arithmetic progression and tan - 1 ⁡ x , tan - 1 ⁡ y and tan - 1 ⁡ z are also in arithmetic progression, then
  32. 32Let S 1 is the complete solution set of the inequality c o s - 1 x c o s - 1 x 2 and S 2 is the complete solution set of the inequality c o
  33. 33The maximum value of x that satisfies the equation s i n - 1 2 15 x = c o s - 1 14 x is
  34. 34The minimum value of x which satisfies the inequality s i n - 1 x 2 ≥ c o s - 1 x 2 is
  35. 35Let f x = s i n - 1 x 1 - x - x 1 - x 2 , 0 x 1 , then f x is
  36. 36The range of the function f x = s i n - 1 x 2 1 + x 2 , x ∈ R is
  37. 37If sin ⁡ cot - 1 ⁡ 1 - x = cos ⁡ tan - 1 ⁡ - x , then x is
  38. 38If the range of f x = t a n - 1 x + 2 s i n - 1 x + c o s - 1 x is a , b , then
  39. 39The domain of the function f x = 2 sin - 1 ⁡ log 2 ⁡ 1 2 x 2 is
  40. 40In a Δ A B C , if ∠ A = ∠ B = 1 2 sin - 1 6 + 1 2 3 + sin - 1 1 3 and length of the side opposite to ∠ C is c = 6 ⋅ 3 1 4 , then the area of
  41. 41Let x + 1 x = 2, y + 1 y = - 2 and sin 1 x + cos 1 y = m , then the value of m is
  42. 42For x ∈ 0 , π 2 , if c o s - 1 7 2 1 + cos ⁡ 2 x + s i n 2 x - 48 c o s 2 x sin ⁡ x = x - cos - 1 k cos ⁡ x , then the value of k is equal t
  43. 43The value of sin ⁡ cot - 1 ⁡ x is
  44. 44The value of the expression cot -1 1 2 + cot -1 9 2 + cot -1 2 5 2 + cot -1 4 9 2 + ....... upto n terms is
  45. 45The value of cos ⁡ tan - 1 ⁡ 3 4 + cos ⁡ tan - 1 ⁡ x is equal to
  46. 46The number of real solutions of cot - 1 ⁡ x x + 4 + cos - 1 ⁡ x 2 + 4 x + 1 = π 2 is equal to
  47. 47The area bounded by the curve y = c o s - 1 sin x + 2 - c o s - 1 cos x and the x -axis, where 2 x , is equal to
  48. 48If sin - 1 2 a 1 + a 2 + sin - 1 2 b 1 + b 2 = 2 cot - 1 1 x , then x is equal to a , b 0 , 1
  49. 49The number of integers for which the equation sin - 1 ⁡ x + cos - 1 ⁡ x + tan - 1 ⁡ x = n has real solution(s) is
  50. 50Consider the function f x = cos - 1 ⁡ 3 x + sin - 1 ⁡ 3 x - 1 , then (where, ⋅ represents the greatest integer part of x )

Frequently Asked Questions

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

This chapter includes 71 NTA Abhyas (JEE Main) questions.

2.Are these questions only from NTA Abhyas (JEE Main), or from other exams too?

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

3.What is the difficulty level of Inverse Trigonometric Functions questions in NTA Abhyas (JEE Main)?

Of the 71 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

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

All of this chapter's questions come from a single topic: Uncategorized.