Chapter 15 · Class 11-12 & JEE Main/Adv
Inverse Trigonometric Functions
28 topics in 14 parts
Principal Value of Inverse Sine Principal Value of Inverse Cosine Principal Value of Inverse Tangent Principal Value of Inverse Cotangent Principal Value of Inverse Secant Principal Value of Inverse Cosecant
Key ideas
Analytical Comparison & Distinction Matrix
| Analytical Method | Standard Representation | Parametric / Invariant Framework |
|---|---|---|
| Algebraic Nature | Explicit equations relating spatial coordinates | Parameterized using scalar parameters (λ, μ) or vectors |
| Symmetry Usage | Relies on coordinate expansion | Exploits vector dot/cross products for rapid simplification |
| Computational Efficiency | Direct for intercept evaluation | Superior for angles, orthogonal projections, and distances |
| Common Mistake | Sign confusion in determinants | Omitting boundary condition checks |
All 28 topics in Inverse Trigonometric Functions
Inverse Functions
- Definition & Existence Conditions
- Domain, Range & Graphs
- Derivative of an Inverse Function
Inverse Trigonometric Functions
- Principal Value Branches & Definitions
- Domain, Range & Graphs
sin⁻¹(sin x) & sin(sin⁻¹x) Type Compositions
- Properties of f(f⁻¹(x)) & f⁻¹(f(x))
- Composite Functions
- Piecewise Graphs & Principal Value Reductions
Relating Different Inverse Trigonometric Functions
- Interconversion of Inverse Trigonometric Functions
- Simplification Using Trigonometric Substitution
- Algebraic & Trigonometric Simplifications
Inverse Functions of −x & 1/x
- Reciprocal Argument Identities
- Negative Argument Identities
sin⁻¹x + cos⁻¹x = π/2 & Other Properties
- Complementary Angle Identities
- Extrema & Boundedness
Sum & Difference of Angles in Terms of tan⁻¹
- Two-Angle Addition & Subtraction Formulas
- Three-Angle Identities & Conditional Simplifications
Multiple Angles in Terms of tan⁻¹x
- Double- & Triple-Angle Formulas
Sum & Difference of Angles in Terms of sin⁻¹ & cos⁻¹
- Addition & Subtraction Formulas
Multiple Angles in Terms of sin⁻¹x & cos⁻¹x
- Double- & Triple-Angle Formulas
sin⁻¹(2x/(1+x²)) & Related Problems
- Trigonometric Substitutions
- Branch-Wise Simplification & Inequalities
Inverse Trigonometric Equations
- Single Equations & Principal Value Solutions
- Simultaneous & Multi-Term Equations
Inverse Trigonometric Inequations
- Basic & Composite Inequalities
Summation of Inverse Trigonometric Series
- Telescoping Arctan Series
- Telescoping Arccot Series
- Infinite & Finite Inverse Trigonometric Sums