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Formula Sheet

Inverse Trigonometric Functions — Formula Sheet

JEE Mains · Mathematics

Free Inverse Trigonometric Functions formula sheet for JEE Mains Mathematics 2026 — all important formulas, equations, and constants for quick reference.

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A clear, organized comparison chart summarizing the domain and principal value range for all six inverse trigonometric functions: arcsin, arccos, arctan, arccosec, arcsec, and arccot.
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Formula Sheet — Inverse Trigonometric Functions

Important formulas and equations from Inverse Trigonometric Functions for JEE Mains Mathematics.

Formulas — Inverse Trigonometric Functions

Domain and Range of Inverse Trigonometric Functions

f(f⁻¹(x)) and f⁻¹(f(x)) — Composition Results

sin(sin⁻¹x) = x, for x ∈ [−1, 1]
sin⁻¹(sin x) = x, only if x ∈ [−π/2, π/2]
cos⁻¹(cos x) = x, only if x ∈ [0, π]
tan⁻¹(tan x) = x, only if x ∈ (−π/2, π/2)
cot⁻¹(cot x) = x, only if x ∈ (0, π)

Negative Argument Properties

sin⁻¹(−x) = −sin⁻¹(x), for x ∈ [−1, 1]
tan⁻¹(−x) = −tan⁻¹(x), for x ∈ ℝ
cosec⁻¹(−x) = −cosec⁻¹(x), for |x| ≥ 1
cos⁻¹(−x) = π − cos⁻¹(x), for x ∈ [−1, 1]
sec⁻¹(−x) = π − sec⁻¹(x), for |x| ≥ 1

Reciprocal Argument Properties

sin⁻¹(1/x) = cosec⁻¹(x), for |x| ≥ 1
cos⁻¹(1/x) = sec⁻¹(x), for |x| ≥ 1
tan⁻¹(1/x) = cot⁻¹(x), if x > 0
tan⁻¹(1/x) = −π + cot⁻¹(x), if x < 0

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Frequently Asked Questions

What topics are covered in Inverse Trigonometric Functions for JEE Mains?
Inverse Trigonometric Functions is an important chapter in JEE Mains Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Concept and Definition of Inverse Functions, Domain and Range of Inverse Trigonometric Functions, Graphs of Inverse Trigonometric Functions, Principal Values and Function Composition.
How important is Inverse Trigonometric Functions for JEE Mains?
Inverse Trigonometric Functions is a frequently tested chapter in JEE Mains Mathematics. Questions from this chapter appear regularly in previous year papers. There are 63 practice questions available for this chapter.
How to prepare Inverse Trigonometric Functions for JEE Mains?
Start by understanding the core concepts, then solve practice questions. Focus on formulas and their applications. Use revision notes for quick review before the exam.

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