Table Of Content8.5 x 11 inch
Trigonometry Booster
13 February 2017 03:31:35 PM
Trigonometry
Booster
with Problems & Solutions
for
JEE
Main and Advanced
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About the Author
REJAUL MAKSHUD (RM)
Post Graduated from Calcutta University in PURE MATHEMATICS.
Presently, he trains IIT Aspirants at RACE IIT Academy, Jamshedpur.
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Trigonometry
Booster
with Problems & Solutions
for
JEE
Main and Advanced
Rejaul Makshud
M. Sc. (Calcutta University, Kolkata)
McGraw Hill Education (India) Private Limited
CHENNAI
McGraw Hill Education Offices
Chennai NewYork St Louis SanFrancisco Auckland Bogotá Caracas
Kuala Lumpur Lisbon London Madrid Mexico City Milan Montreal
San Juan Santiago Singapore Sydney Tokyo Toronto
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McGraw Hill Education (India) Private Limited
Published by McGraw Hill Education (India) Private Limited
444/1, Sri Ekambara Naicker Industrial Estate, Alapakkam, Porur, Chennai - 600 116
Coordinate Geometry Booster
Copyright © 2017, McGraw Hill Education (India) Private Limited.
No part of this publication may be reproduced or distributed in any form or by any means, electronic, mechanical,
photocopying, recording, or otherwise or stored in a database or retrieval system without the prior written permission
of the publishers. The program listings (if any) may be entered, stored and executed in a computer system, but they
may not be reproduced for publication.
This edition can be exported from India only by the publishers,
McGraw Hill Education (India) Private Limited
ISBN (13): 978-93-5260-248-3
ISBN (10): 93-5260-248-X
Information contained in this work has been obtained by McGraw Hill Education (India), from sources believed to be
reliable. However, neither McGraw Hill Education (India) nor its authors guarantee the accuracy or completeness
of any information published herein, and neither McGraw Hill Education (India) nor its authors shall be responsible
for any errors, omissions, or damages arising out of use of this information. This work is published with the
understanding that McGraw Hill Education (India) and its authors are supplying information but are not attempting
to render engineering or other professional services. If such services are required, the assistance of an appropriate
professional should be sought.
Typeset at The Composers, 260, C.A. Apt., Paschim Vihar, New Delhi 110 063 and text and cover printed at
Cover Designer: Creative Designer
visit us at: www.mheducation.co.in
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Dedicated to
My Parents
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Preface
TRIGONOMETRY BOOSTER with Problems & Solutions for JEE Main and Advanced is meant for aspirants preparing for the
entrance examination of different technical institutions, especially NIT/IIT/BITSAT/IISc. In writing this book, I have drawn
heavily from my long teaching experience at National Level Institutes. After many years of teaching I have realised the need
of designing a book that will help the readers to build their base, improve their level of mathematical concepts and enjoy the
subject.
This book is designed keeping in view the new pattern of questions asked in JEE Main and Advanced Exams. It has five
chapters. Each chapter has the concept booster followed by a large number of exercises with the exact solutions to the problems
as given below:
Level - I : Problems based on Fundamentals
Level - II : Mixed Problems (Objective Type Questions)
Level - III : Problems for JEE Advanced Exam
Level - IV : Tougher Problems for JEE Advanced Exams
(0.......9) : Integer type Questions
Passages : Comprehensive Link Passages
Matching : Matrix Match
Reasoning : Assertion and Reason
Previous years papers : Questions asked in Previous Years’ IIT-JEE Exams
Remember friends, no problem in mathematics is difficult. Once you understand the concept, they will become easy. So
please don’t jump to exercise problems before you go through the Concept Booster and the objectives. Once you are confident
in the theory part, attempt the exercises. The exercise problems are arranged in a manner that they gradually require advanced
thinking.
I hope this book will help you to build your base, enjoy the subject and improve your confidence to tackle any type of
problem easily and skilfully.
My special thanks goes to Mr. M.P. Singh (IISc. Bangalore), Mr. Manoj Kumar (IIT, Delhi), Mr. Nazre Hussain (B. Tech.),
Dr. Syed Kashan Ali (MBBS) and Mr. Shahid Iqbal, who have helped, inspired and motivated me to accomplish this task. As
a matter of fact, teaching being the best learning process, I must thank all my students who inspired me most for writing this
book.
I would like to convey my affectionate thanks to my wife, who helped me immensely and my children who bore with
patience my neglect during the period I remained devoted to this book.
I also convey my sincere thanks to Mr Biswajit Das of McGraw Hill Education for publishing this book in such a beautiful
format.
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viii Preface
I owe a special debt of gratitude to my father and elder brother, who taught me the first lesson of Mathematics and to all my
learned teachers— Mr. Swapan Halder, Mr. Jadunandan Mishra, Mr. Mahadev Roy and Mr. Dilip Bhattacharya, who instilled
the value of quality teaching in me.
I have tried my best to keep this book error-free. I shall be grateful to the readers for their constructive suggestions toward
the improvement of the book.
Rejaul Makshud
M. Sc. (Calcutta University, Kolkata)
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Contents
Preface vii
Chapter 1 The Ratios and Identities 1.1–1.87
Introduction 1.1
Measurement of Angles 1.1
Trigonometrical Ratios 1.2
Limits of the values of Trigonometrical Functions 1.2
Sign of Trigonometric Ratios 1.2
T-ratios of the Angle (–q), in Terms of q, for All Values of q 1.3
T-ratios of the Different Angles in Terms of q, for All Values of q 1.3
Graph of Trigonometric Functions 1.3
T-ratios of Compound Angles 1.4
Some Important Deductions 1.4
Transformation Formulae 1.5
Multiple Angles 1.6
Some Important Deductions 1.6
The Maximum and Minimum Values of 1.7
Sub–Multiple Angles 1.8
Conditional Trigonometrical Identities 1.11
Trigonometrical Series 1.12
Exercises 1.12
Answers 1.30
Hints and Solutions 1.30
Chapter 2 Trigonometric Equations 2.1–2.53
Definition 2.1
Solution of a Trigonometric Equation 2.1
General solution of Trigonometric Equations 2.1
A Trigonometric Equation is of the Form 2.1
Principal Value 2.1
Method to Find Out the Principal Value 2.2
Solutions in Case of Two Equations are Given 2.2
Some Important Remarks to Keep in Mind while Solving a Trigonometric Equation 2.2
Types of Trigonometric Equations: 2.2
Exercises 2.3
Answers 2.17
Hints and Solutions 2.18
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