Solving Problems In Algebra And Trigonometry | V. Litvinenko, A. Mordkovich

In this post, we will see the book Solving Problems In Algebra and Trigonometry – V. Litvinenko, A. Mordkovich. 

About the book:

This study aid is intended for students of physical and mathemati­cal faculties of pedagogical institutes.
The book contains about 2000 examples, problems, and exercises of which 1700 problems are for solving independently. Along with rather simple problems, there are also problems whose solution requires serious and sometimes inventive work. In the course of preparing the manuscript for print we tried to distribute the space among the basic types of “school” problems in algebra and trigonom­etry. Solving these problems will help the student to acquire pro­fessional skill necessary for a teacher who must know how to solve mathematical problems of the high-school level.
This book is not only a collection of problems, it is rather a study aid for practical work, as can be seen in the structure of the text­ book. Each section contains necessary theoretical material and an ample number of worked examples (the total number of which amounts to about 300), which are very useful for the student pri­ marily from the methodological point of view.

The book was translated from the Russian by Leonid Levant and was first published by Mir in 1987.

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Contents

PART 1. ALGEBRA 7

Chapter 1. IDENTICAL TRANSFORMATIONS 7

Sec. 1. Factorization of Polynomials 7
Sec. 2. Identical Transformations of Rational Functions 11
Sec. 3. Identical Transformations of Irrational Functions 20
Sec. 4. Identical Transformations of Exponential and Logarith­mic Functions 29
Sec. 5. Proving Inequalities 33
Sec. 6. Comparing Numerical Expressions 41

Chapter 2. SOLVING EQUATIONS AND INEQUALITIES 45

PART II. TRIGONOMETRY 202

Chapter 3. IDENTICAL TRANSFORMATIONS 202

Sec. 21. Identical Transformations of Trigonometric Functions 202
Sec. 22. Transforming Functions Containing Inverse Trigonometric Functions 218
Sec. 23. Proving Inequalities 224

Chapter 4. SOLVING EQUATIONS AND INEQUALITIES 234

Sec. 24. Equations 234
Sec. 25. Systems of Equations 254
Sec. 26. Inequalities 265
Sec. 27. Parametric Equations and Inequalities 276

Answers 287