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Inverse Trigonometric Functions — Formula Sheet

GUJCET · Mathematics

All important formulas from Inverse Trigonometric Functions for GUJCET Mathematics. Quick reference for revision and problem solving.

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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 GUJCET 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 GUJCET?
Inverse Trigonometric Functions is an important chapter in GUJCET 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 GUJCET?
Inverse Trigonometric Functions is a frequently tested chapter in GUJCET Mathematics. Questions from this chapter appear regularly in previous year papers. There are 222 practice questions available for this chapter.
How to prepare Inverse Trigonometric Functions for GUJCET?
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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