Inverse Trigonometric Functions for JEE

• sin⁻¹x has range [−π/2, π/2]; cos⁻¹x has [0, π]
• sin⁻¹x + cos⁻¹x = π/2
• sin(sin⁻¹x) = x always for x in [−1, 1]; sin⁻¹(sin x) = x only in the principal range
• Convert all terms to one function before simplifying

• tan⁻¹x + tan⁻¹y = tan⁻¹((x + y)/(1 − xy)) for xy < 1
• 2tan⁻¹x = sin⁻¹(2x/(1 + x²)) for |x| ≤ 1
• tan⁻¹x + cot⁻¹x = π/2
• sin⁻¹(−x) = −sin⁻¹x, cos⁻¹(−x) = π − cos⁻¹x

Printable Inverse Trigonometric Functions formula sheet: formulas, key ideas and traps on one page. Save it as a PDF for offline revision.

• Ignoring principal ranges
• Using sum formulas outside their conditions
• Sign errors for negative arguments

Appears regularly; quick marks. Usually one question. Principal value traps are the most common mistake.

Prerequisites: Trigonometry (Ratios, Identities, Equations).

Chapter names follow the current rationalised NCERT textbooks. Read these sections before solving PYQs.

Question. If sin⁻¹(x) + sin⁻¹(y) + sin⁻¹(z) = 3π/2, find the value of x²y² + y²z² + z²x² + 2x²y²z².

This example was solved twice independently and both solutions agree.

Full-chapter free lectures picked from YouTube search results by views, from established JEE channels (mostly in Hinglish). Use the subtopic list to jump straight to the part you need (timestamps come from each video's own chapter list). Watch one, then solve PYQs the same day.

• INVERSE TRIGONOMETRIC FUNCTIONS in One Shot: All Concepts & PYQs Covered | JEE Main & Advanced — JEE Wallah, 5:56:24
  Jump to a subtopic (22)

  • 00:00 Introduction
  • 05:11 Topics to be covered
  • 06:45 Defining I.T.F.
  • 26:00 Domain & Range of I.T.F.
  • 1:02:00 Graphs of I.T.F.
  • 1:29:28 Properties of I.T.F
  • 1:33:10 Property 2
  • 1:40:51 Property 3
  • 2:07:02 Property 4
  • 2:17:56 Property 5
  • 2:27:10 Property 6
  • 2:32:20 Property 7
  • 3:08:27 Property 8
  • 3:24:37 Solving Inverse Trigo Equations
  • 3:44:50 Break
  • 4:24:35 Solving Inverse Trigo In-equations
  • 4:32:10 Problems on Telescoping Series
  • 4:56:32 Important Graphs
  • 5:23:26 Double angle Formulas
  • 5:53:26 Triple angle Formulas
  • 5:54:10 Homework
  • 5:56:18 Thank you bachhon
• Inverse Trigonometric Functions | One Shot | #BounceBack Series | Unacademy Atoms | Nishant Vora — JEE Legends, 4:43:04
  Jump to a subtopic (7)

  • 00:00 Introduction
  • 07:18 Inverse Trigonometric Functions
  • 36:12 Basic Questions
  • 49:17 Domain and Range Questions
  • 1:18:50 Properties of ITF
  • 3:16:42 Transformation by Substitution
  • 3:50:35 Summation of Series

• 4 JEE Main 2026 PYQs on Inverse Trigonometric Functions, with solutions.
• Read the chapter in NCERT textbooks (official, free), then solve its NCERT Exemplar (official, free) questions.
• Chapter-wise past questions: JEE Main and Advanced PYQs and question bank.
• Timed practice tests: NTA Abhyas practice tests (official, free) and our free mock tests.
• See it move: interactive simulation.