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Inverse Trigonometric Functions

NCERT Class 12 Mathematics Chapter 2

Inverse Trigonometric Functions for Class 12 Maths and JEE: domains, ranges and principal value branches, graphs, principal values and simple properties.

2 topics Updated 8 Nov 2026

For: Class 12 and JEE

In the syllabus: JEE Class 12 syllabus

With your textbook

NCERT Mathematics Part I (Class 12), Chapter 2 “Inverse Trigonometric Functions”, reprint 2026-27.

Open the official NCERT chapter (PDF, 1.4 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Inverse trigonometric functions and their principal value branches

    Inverse trigonometric functions for Class 12 Maths and JEE: domain and range of each principal value branch, graphs, principal values and solved examples.

    NCERT Sections 2.1–2.2 14 min read 5 solved examples 10 practice questions

  2. Properties of inverse trigonometric functions

    Properties of inverse trigonometric functions for Class 12 Maths and JEE: sin(sin x) for any x, substitutions, formulas for JEE and solved examples.

    NCERT Section 2.3 17 min read 6 solved examples 16 practice questions

Key formulas in this chapter

Principal value branches

  • sin: [−1, 1] → [−π/2, π/2]
  • cos: [−1, 1] → [0, π]
  • tan: R → (−π/2, π/2)
  • cot: R → (0, π)
  • cosec: R − (−1, 1) → [−π/2, π/2] − {0}
  • sec: R − (−1, 1) → [0, π] − {π/2}
  • y = sin x ⇔ sin y = x and −π/2 ≤ y ≤ π/2

Properties

  • sin(sin x) = x, for x ∈ [−1, 1]
  • sin(sin x) = x, for x ∈ [−π/2, π/2]
  • cos(cos x) = x, for x ∈ [0, π]
  • tan(tan x) = x, for x ∈ (−π/2, π/2)
  • sin x + cos x = π/2 (|x| ≤ 1); tan x + cot x = π/2 (x real)
  • tan x + tan y = tan((x + y)/(1 − xy)), for xy < 1

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