Inverse Trigonometric Functions — JEE Main Previous Year Questions

How many JEE Main questions come from Inverse Trigonometric Functions?

Inverse Trigonometric Functions has contributed 90 questions to Joint Entrance Examination (Main) papers between 2017 and 2026 — an average of about 10 questions a year. That count is measured from EByAi’s bank of 55,289 JEE Main questions, not estimated from a syllabus. Every one of the 90 questions carries a written, step-by-step solution, and each is tagged to Inverse Trigonometric Functions within Mathematics, so you can drill this chapter across every year at once instead of hunting through paper PDFs. Practising a chapter’s full PYQ history is the fastest way to learn the patterns examiners reuse.

Sample Inverse Trigonometric Functions questions from real JEE Main papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 90 Inverse Trigonometric Functions questions (with full written solutions) are available in practice.

1. Question 1 · JEE Main 2026

   The number of solutions of ${\tan }^{-1}4x+{\tan }^{-1}6x=\frac{\pi }{6}$, where $-$\frac{1}{2\sqrt{6}}$
   1. (A)2
   2. (B)0
   3. (C)3
   4. (D)1
   Show answerAnswer

   Answer: (D) 1

2. Question 2 · JEE Main 2026

   If $\sin \left({\tan }^{-1}(x\sqrt{2})\right)=\cot \left({\sin }^{-1}\sqrt{1-x^2}\right),x\in (0,1)$, then the value of $x$ is:
   1. (A)$\frac{1}{2}$
   2. (B)$\frac{1}{3}$
   3. (C)$\frac{2}{3}$
   4. (D)$\frac{5}{8}$
   Show answerAnswer

   Answer: (A) $\frac{1}{2}$

3. Question 3 · JEE Main 2026

   Considering the principal values of inverse trigonometric functions, the value of the expression $\tan \left(2{\sin }^{-1}\left(\frac{2}{\sqrt{13}}\right)-2{\cos }^{-1}\left(\frac{3}{\sqrt{10}}\right)\right)$ is equal to :
   1. (A)$\frac{33}{56}$
   2. (B)$-\frac{33}{56}$
   3. (C)$-\frac{16}{63}$
   4. (D)$\frac{16}{63}$
   Show answerAnswer

   Answer: (A) $\frac{33}{56}$

4. Question 4 · JEE Main 2025

   $\cos \left({\sin }^{-1}\frac{3}{5}+{\sin }^{-1}\frac{5}{13}+{\sin }^{-1}\frac{33}{65}\right)$ is equal to:
   1. (A)$\frac{33}{65}$
   2. (B)1
   3. (C)$\frac{32}{65}$
   4. (D)0
   Show answerAnswer

   Answer: (D) 0

5. Question 5 · JEE Main 2025

   Let [x] denote the greatest integer less than or equal to x. Then the domain of $f(x)={\sec }^{-1}(2[x]+1)$ is:
   1. (A)$(-\infty ,\infty )$
   2. (B)$(-\infty ,\infty )-\{0\}$
   3. (C)$(-\infty ,-1]\cup [0,\infty )$
   4. (D)$(-\infty ,-1]\cup [1,\infty )$
   Show answerAnswer

   Answer: (A) $(-\infty ,\infty )$

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