Fundamentals of Mathematics for Jee Main and Advanced Trigonometry by Sanjay Mishra is an essential resource for students preparing for the Joint Entrance Examination (JEE) Main and Advanced. This book is designed to help students understand the fundamentals of mathematics and strengthen their problem-solving skills.

The book covers a wide range of topics, including algebra, trigonometry, calculus, and geometry, all of which are crucial for success in the JEE Main and Advanced. The author, Sanjay Mishra, has years of experience teaching mathematics to JEE aspirants and has developed a unique approach to simplifying complex concepts.

One of the most important sections of the book is the coverage of Trigonometry. This section delves deep into the subject and covers topics such as properties of triangles, inverse trigonometric functions, and trigonometric equations. The author has used numerous examples and exercises to help students understand the concepts better. Additionally, the book provides shortcuts and tricks to solve problems quickly, which can be a valuable asset for students during the JEE exams.

**TABLE OF CONTENTS**

**Chapter 1 Trigonometric Ratios and Identities**

- Angles and Measurements
- Polygon and its properties
- Quadrants and Its Sign Conventions
- Sign Convention of Angle
- Domain and Range of Function
- Periodicity and Periodic Functions
- Properties of Eriodicity
- Even Function
- Properties of Even Function
- Odd Function
- Trigonometric Ratios and their properties
- Sign of Trigonometric Ratios
- Trigonometric Identities
- Pythagorian Identities
- Trigonometric Ratios of some specific angles
- Trigonometric ratios of 45
- Trigonometric ratios of 30 and 60
- Trigonometric ratios of 0 and 90
- Sinx and Cosec x
- Cos x and Sec x
- Tanx and Cot x
- Trigonometric Ratios for Allied Angles
- Inter-conversion of Trigonometric Ratios
- Formula on Trigonometric Ratios of Compound Angles
- Intercept Application of Submultiple of an angle
- Sum and difference of Tangent and Cotangents
- Conversion Formulae
- Trigonometric Ratios of the sum of three or more angles
- Conditional Identities
- Application of Trigonometry for Eliminating Variables
- Maximum and Minimum values of Trigonometric Functions
- Application of Theory of Equation
- Applications based on Quadratic Equation
- Application Using Transformation of Equations
- Proving Trigonometric Inequalities
- Jenson’s Functional Equation and Inequality and its applications
- Summation of Series containing sine and cosine angles forming an A.P
- Sine of angle forming an AP
- Cosine of Angle Forming an AP
- Application of Complex Numbers for Sum of Trigonometric Series
- Series containing Product of Cosine of the Angles Forming a G.P

**Chapter 2 Trigonometric Equations**

- Solution of Trigonometric Equations
- Particular Solution
- Principal Solution
- General Solution
- Equivalent Equations
- Sources of Extraneous Root and loss of Root
- Trigonometric Equation of some special Forms
- Solving Simultaneous Equations
- Equations with only one variable
- Equations with two or more variables
- Problems based on Extreme values of sin x and cos x
- Trigonometric Equations involving single variable
- Trigonometric Equations involving more than one variable
- Transcendental Equations
- Graphical Solutions of Equations
- Solving Inequalities
- Review of some Important Trigonometric Values

**Chapter 3 Properties and Solution of Triangle**

- Properties of Triangle
- Solution of Triangle
- Sine Formula
- Applications of Sine Formula
- Cosine Formula
- Applications of Cosine Formula
- Projection Formula
- Napier’s Analogy
- To find the Sine, Cosine, and Tangent of the Half angles in terms of the sides
- Area of Triangle ABC
- m-n Theorem (Cotangent Theorem)
- Solution of Triangle
- Geometrical Discussion
- Centroid of Triangle and Length of Median
- Length of Medians
- The angles that the median makes with sides
- Circumcircle and Circumcentre of triangle
- Incircle of a Trangle
- Escribed Circles
- Orthocentre, Pedal Triangle and its properties
- Circumcircle of Pedal Triangle
- Properties of Nine Point Circle
- The Ex-central Triangle
- The Centroid lies on the line joining the circumcentre to the orthocenter
- The length of angle Bisector and the angle that the bisector makes with the sides
- The perimeter and area of a regular polygon of n-side inscribed n a circle
- The perimeter and area of a regular polygon of n-sides Circumscribed about a given circle
- The radii of the Inscribed and Circumscribing circles of a regular polygon

**Chapter 4 Inverse Trigonometric Functions**

- Inverse Functions
- Inverse Trigonometric Functions
- Graphs of Inverse Circular Functions of their corresponding Trigonometric Functions in principal domain
- Inverse Circular Functions of their corresponding Trigonometric Functions in Complete Domain
- Inverse Trigonometric Functions of Negative inputs
- Inverse Trigonometric Functions of reciprocal Inputs
- Inter Conversion of Inverse Trigonometric Functions
- Three important Identities of Inverse Trigonometric Functions
- Multiples of Inverse Trigonometric Functions
- Sum and Difference of Inverse Trigonometric Functions

.

.

The book also includes a wide range of practice problems and previous years’ JEE questions, which can help students develop a better understanding of the exam pattern and improve their problem-solving abilities. The solutions to the problems are provided at the end of the book, making it easy for students to check their answers and identify their weak areas.

Furthermore, the book is available in PDF format, making it easily accessible to students. Students can download it from various online platforms, and it can be accessed on any device. This feature makes it easy for students to study on the go, allowing them to make the most of their time.

In conclusion, Fundamentals of Mathematics for JEE Main and Advanced Trigonometry by Sanjay Mishra is an excellent resource for JEE aspirants. The book covers essential topics and provides students with the necessary tools to succeed in exams. Additionally, the availability of the book in PDF format makes it accessible to students, allowing them to study whenever and wherever they want.