Chapter 31 · Class 11-12 & JEE Main/Adv
Trigonometric Ratios & Identities
72 topics in 15 parts
Pythagorean identity Double-angle sine Basic Trigonometric Ratios Reciprocal Identities Quotient Identities Pythagorean Identity
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 72 topics in Trigonometric Ratios & Identities
Trigonometric Ratios & Functions
- Definitions of Trigonometric Ratios
- Fundamental Trigonometric Identities
- Trigonometric Identity Simplification
- Functions of Any Angle
- Circular Functions & Unit Circle
- Standard-Angle Values
- Exact Value Evaluation
- Use of Trigonometry in Geometry
- Mixed Trigonometric Concepts
Measurement of an Angle
- Degree Measure
- Radian Measure
- Degree–Radian Conversion
- Common Angle Conversions
- Radians & Real Numbers
- Arc Length & Chord Applications
Angles of Trigonometry
- Angles Beyond One Revolution
- Reference Angles
- Signs of Angles
- Signs in Different Quadrants
- Variation Across Quadrants
- Allied Angles
Graphs of Trigonometric Functions
- Graphs & Interpretation
- Transformations of Graphs
- Graphical Solutions of Equations
- Mixed Graph Applications
Compound Angles
- Sine of Sum & Difference
- Cosine of Sum & Difference
- Tangent of Sum & Difference
- Expressions of Type A Cos θ ± B Sin θ
- Sin² A − Sin² B & Similar Formulae
- Componendo & Dividendo
- Cotangent Identities
- Mixed Compound-Angle Identities
Transformation Formulae
- Product-to-Sum Formulae
- Sum-to-Product Formulae
Multiple & Submultiple Angles
- Double & Triple-Angle Formulae
- Multiple-Angle Formulae
- Half-Angle & Submultiple-Angle Formulae
- Identities Involving 1 ± Cos 2A & 1 ± Sin 2A
- Nested-Radical Half-Angle Forms
Values of Trigonometric Ratios of Typical Angles
- 15° & 75°
- 18°, 36°, 54° & 72°
- 22.5° & 67.5°
- Other Special Angles
- Mixed Special-Angle Values
Continued Products of Sine, Cosine & Tangent
- Cos A Cos(60° − A) Cos(60° + A)
- Sin A Sin(60° − A) Sin(60° + A)
- Tan A Tan(60° − A) Tan(60° + A)
- Products of Sines & Tangents
- Complementary-Angle Tangent Products
- Logarithmic Product Identities
Conditional Identities
- Standard Triangle Identities
- Maximum & Minimum Values Related to Triangles
- Sum-of-Squares Identities
- Trigonometric Quantities in AP & GP
- Systems of Conditional Identities
- General Conditional Identities
Heights & Distances
- Angles of Elevation & Depression
Range, Maxima & Minima
- Boundedness of Trigonometric Functions
- Range by Various Methods
- Range of A Cos θ + B Sin θ
- Maxima & Minima of Trigonometric Expressions
- Maxima & Minima Under Constraints
- Inequalities & Bounds
Trigonometric Series
- Sums of Trigonometric Series
- Telescoping Trigonometric Series
- Special Trigonometric Series
Trigonometric Equations & Inequations
- Trigonometric Equations
- General Solution of Trigonometric Equations
- Systems of Trigonometric Equations
- Trigonometric Inequations
Trigonometric Limits
- Evaluation of Trigonometric Limits