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Mathematics - Inverse Trigonometric Functions

Practise 14 JEE Advanced previous year questions on Inverse Trigonometric Functions, compiled from papers spanning 2007 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 Advanced tests.

Inverse Trigonometric Functions has been asked in 12 of the 27 years of JEE Advanced papers analysed (2000–2026), with 14 questions in all. 29% of them were easy, 64% moderate and 7% tough. Most of its questions came from 2014, with 2 questions that year. In the last three years (2024–2026) it had 3 questions across 6 papers, about 0.5 per paper.

The chapter's 7 topics are not weighted equally: T inverse T property (3 questions, 21%), Principal Value and Basics (3 questions, 21%), and Converting one Inverse T function to other Inverse T (2 questions, 14%) have been asked the most. Over the last five years the most frequent topics have been Principal Value and Basics (2), T inverse T property (1), and Sum and difference of angles (1). Sum and difference of angles has produced the most tough questions (1).

  1. 1Considering only the principal values of the inverse trigonometric functions, the value of is2026 (Paper 1)Principal Value and Basics
  2. 2The total number of real solutions of the equation is (Here, the inverse trigonometric functions and assume values in and , respectively.)2025 (Paper 2)T inverse T property
  3. 3Considering only the principal values of the inverse trigonometric functions, the value of is2024 (Paper 2)Principal Value and Basics
  4. 4Considering only the principal values of the inverse trigonometric functions, the value of 3 2 cos - 1 2 2 + 2 + 1 4 sin - 1 2 2 2 + 2 + tan2022 (Paper 1)Sum and difference of angles
  5. 5For any positive integer n , let S n : ( 0 , ) R be defined by S n x = k = 1 n cot - 1 1 + k ( k + 1 ) x 2 x where for any x R , cot - 1 ( x2021 (Paper 1)Infinite Series
  6. 6For any positive integer n , define f n : 0 , R as f n x = i = 1 n tan - 1 1 1 + x + j x + j - 1 for all x 0 , . ( Here, the inverse trigono2018 (Paper 2)Infinite Series
  7. 7If = 3 sin - 1 6 11 a n d = 3 cos - 1 4 9 , where the inverse trigonometric functions take only the principal values, then the correct optio2015 (Paper 2)Principal Value and Basics
  8. 8Let f : 0 , 4 0 , be defined by f x = cos - 1 cos x . The number of points x 0 , 4 satisfying the equation f x = 10 - x 10 is_________2014 (Paper 1)T inverse T property
  9. 9Match the following. List I List II (A) Let y x = cos 3 cos - 1 x , x - 1 , 1 , x 3 2 . Then 1 y x x 2 - 1 d 2 y x d x 2 + x d y x d x equal2014 (Paper 2)Sum and difference of angles
  10. 10The value of c o t n = 1 2 3 cot - 1 1 + k = 1 n 2 k is2013 (Paper 1)Sum of complementary angles
  11. 11Match List I with List II and select the correct answer using the code given below the lists : List - I List - II A. 1 y 2 cos tan - 1 y + y2013 (Paper 2)Multiple Angles
  12. 12Let , where . Then, the value of is2011 (Paper 1)Converting one Inverse T function to other Inverse T
  13. 13If , then is equal to2008 (Paper 1)Converting one Inverse T function to other Inverse T
  14. 14Let be such that . Match the statements in Column I with the values in Column II.2007 (Paper 2)T inverse T property

Frequently Asked Questions

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

This chapter includes 14 questions compiled from JEE Advanced papers spanning 2007 to 2026.

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

These are JEE Advanced 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 JEE Advanced Mathematics?

Inverse Trigonometric Functions has appeared in 12 of the 21 years of JEE Advanced papers covered here, with 14 questions across 14 papers - about one per paper it appears in.

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

Of the 14 questions analysed for this chapter, 29% are easy, 64% moderate and 7% tough. 2014 had the most, with 2 questions.

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

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

  • T inverse T property - 3 questions (21%)
  • Principal Value and Basics - 3 questions (21%)
  • Converting one Inverse T function to other Inverse T - 2 questions (14%)
  • Sum and difference of angles has produced the most tough questions (1).
6.Is Inverse Trigonometric Functions's weightage in JEE Advanced going up or down?

Across all 14 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.