Topics
Mathematical Logic
- Statements and Truth Values in Mathematical Logic
- Logical Connectives
- Tautology, Contradiction, and Contingency
- Quantifier, Quantified and Duality Statements in Logic
- Negations of Compound Statements
- Converse, Inverse, and Contrapositive
- Algebra of Statements
- Application of Logic to Switching Circuits
- Overview of Mathematical Logic
Matrices
Trigonometric Functions
Pair of Straight Lines
Vectors
Line and Plane
Linear Programming
Differentiation
- Introduction & Derivatives of Some Standard Functions
- Derivative of Composite Functions
- Geometrical Meaning of Derivative
- Derivative of Inverse Function
- Logarithmic Differentiation
- Derivatives of Implicit Functions
- Derivatives of Parametric Functions
- Higher Order Derivatives
- Overview of Differentiation
Applications of Derivatives
- Applications of Derivatives in Geometry
- Derivatives as a Rate Measure
- Approximations
- Rolle's Theorem
- Lagrange's Mean Value Theorem (LMVT)
- Increasing and Decreasing Functions
- Maxima and Minima
- Overview of Applications of Derivatives
Indefinite Integration
- Indefinite Integration with Standard Indefinite Integral Formulae
- Methods of Integration> Integration by Substitution
- Methods of Integration> Integration by Parts
- Methods of Integration> Integration Using Partial Fraction
- Overview of Indefinite Integration
Definite Integration
- Definite Integral as Limit of Sum
- Integral Calculus
- Methods of Evaluation and Properties of Definite Integral
- Overview of Definite Integration
Application of Definite Integration
- Application of Definite Integration
- Area Bounded by Two Curves
- Overview of Application of Definite Integration
Differential Equations
- Differential Equations
- Order and Degree of a Differential Equation
- Formation of Differential Equations
- Homogeneous Differential Equations
- Linear Differential Equations
- Applications of Differential Equation
- Solution of a Differential Equation
- Overview of Differential Equations
Probability Distributions
- Random Variables
- Probability Distribution of Discrete Random Variables
- Probability Distribution of a Continuous Random Variable
- Variance of a Random Variable
- Expected Value and Variance of a Random Variable
- Overview of Probability Distributions
Binomial Distribution
- Bernoulli Trial
- Mean and Variance of Binomial Distribution
- Probability using Binomial Distribution
- Overview of Binomial Distribution
Estimated time: 6 minutes
- Trigonometric equation
- Solution of Trigonometric equation
- Principal Solutions
- The General Solution
Maharashtra State Board: Class 12
Definition: Trigonometric Equation
An equation involving trigonometric functions of a variable is called a trigonometric equation.
e.g. cos²θ − sinθ = 1/2, tan mθ = cot nθ, etc. are trigonometric equations.
Maharashtra State Board: Class 12
Key Points: Types of Solution
| Type of Solution | Description |
|---|---|
| Principal Solution | A solution of a trigonometric equation in the interval 0 ≤ θ < 2π |
| General Solution | Solution obtained by using the periodicity of trigonometric functions |
| Particular Solution | A specific solution that satisfies the given conditions |
Maharashtra State Board: Class 12
Formula: General Solution
| Trigonometric Equation | General Solution |
|---|---|
| i. sinθ = 0 | θ = nπ, n ∈ Z |
| ii. cosθ = 0 | θ = (2n + 1)π/2, n ∈ Z |
| iii. tanθ = 0 | θ = nπ, n ∈ Z |
| iv. sinθ = sinα | θ = nπ + (−1)ⁿα, n ∈ Z |
| v. cosθ = cosα | θ = 2nπ ± α, n ∈ Z |
| vi. tanθ = tanα | θ = nπ + α, n ∈ Z |
| vii. sin²θ = sin²α cos²θ = cos²α tan²θ = tan²α | θ = nπ ± α, n ∈ Z |
| viii. a cosθ + b sinθ = c where a, b, c ≠ 0 and a, b, c ∈ R |
θ = 2nπ + α ± β \[\sin\alpha=\frac{b}{\sqrt{a^{2}+b^{2}}}\] \[\cos\beta=\frac{c}{\sqrt{a^{2}+b^{2}}}\] |
