Angle and Its Measurement
Trigonometry - 1
- Introduction of Trigonometry
- Trigonometric Functions with the Help of a Circle
- Signs of Trigonometric Functions in Different Quadrants
- Range of Cosθ and Sinθ
- Trigonometric Functions of Specific Angles
- Trigonometric Functions of Negative Angles
- Fundamental Identities
- Periodicity of Trigonometric Functions
- Domain and Range of Trigonometric Functions
- Graphs of Trigonometric Functions
- Polar Co-ordinate System
Trigonometry - 2
- Trigonometric Functions of Sum and Difference of Angles
- Trigonometric Functions of Allied Angels
- Trigonometric Functions of Multiple Angles
- Trigonometric Functions of Double Angles
- Trigonometric Functions of Triple Angle
- Factorization Formulae
- Formulae for Conversion of Sum Or Difference into Product
- Formulae for Conversion of Product in to Sum Or Difference
- Trigonometric Functions of Angles of a Triangle
Determinants and Matrices
- Definition and Expansion of Determinants
- Minors and Cofactors of Elements of Determinants
- Properties of Determinants
- Application of Determinants
- Cramer’s Rule
- Consistency of Three Equations in Two Variables
- Area of Triangle and Collinearity of Three Points
- Introduction to Matrices
- Types of Matrices
- Algebra of Matrices
- Properties of Matrix Multiplication
- Properties of Transpose of a Matrix
Measures of Dispersion
Sequences and Series
Permutations and Combination
Methods of Induction and Binomial Theorem
Sets and Relations
- Properties of the factorial notation:
For any positive integers m, n.,
1) n! = n × (n - 1)!
2) n > 1, n! = n × (n - 1) × (n - 2)!
3) n > 2, n! = n × (n - 1) × (n - 2) × (n - 3)!
4) (m + n)! is always divisible by m! as well as by n!
5) (m × n)! ≠ m! × n!
6) (m + n)! ≠ m! + n!
7) m > n, (m - n)! ≠ m! - n! but m! is divisible by n!
8) (m ÷ n)! ≠ m! ÷ n
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