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Formula Sheet

Inverse Trigonometric Functions — Formula Sheet

AEEE · Mathematics

Free Inverse Trigonometric Functions formula sheet for AEEE 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 AEEE Mathematics.

Formulas — Inverse Trigonometric Functions

Basic Definitions and Domains/Ranges

y = sin⁻¹x ⟺ x = sin y, where y ∈ [-π/2, π/2]
y = cos⁻¹x ⟺ x = cos y, where y ∈ [0, π]
y = tan⁻¹x ⟺ x = tan y, where y ∈ (-π/2, π/2)

Fundamental Properties and Identities

sin⁻¹x + cos⁻¹x = π/2
tan⁻¹x + cot⁻¹x = π/2
sin⁻¹(-x) = -sin⁻¹x
cos⁻¹(-x) = π - cos⁻¹x

Addition and Subtraction Formulas

sin⁻¹x + sin⁻¹y = sin⁻¹(x√(1-y²) + y√(1-x²))
cos⁻¹x + cos⁻¹y = cos⁻¹(xy - √(1-x²)√(1-y²))
tan⁻¹x + tan⁻¹y = tan⁻¹((x+y)/(1-xy))
tan⁻¹x - tan⁻¹y = tan⁻¹((x-y)/(1+xy))

Multiple Angle Formulas

2tan⁻¹x = sin⁻¹(2x/(1+x²))
2tan⁻¹x = cos⁻¹((1-x²)/(1+x²))
2tan⁻¹x = tan⁻¹(2x/(1-x²))
2sin⁻¹x = sin⁻¹(2x√(1-x²))

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Frequently Asked Questions

What topics are covered in Inverse Trigonometric Functions for AEEE?
Inverse Trigonometric Functions is an important chapter in AEEE Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Basic Concepts and Definitions, Properties and Identities, Solving Equations with Inverse Trigonometric Functions, Graphical Properties and Analysis.
How important is Inverse Trigonometric Functions for AEEE?
Inverse Trigonometric Functions is a frequently tested chapter in AEEE Mathematics. Questions from this chapter appear regularly in previous year papers. There are 254 practice questions available for this chapter.
How to prepare Inverse Trigonometric Functions for AEEE?
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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