在许多代数问题中,根据有关字母的取值范围或满足的条件,引进相应的三角函数,借用三角方法解答这些问题,往往比纯代数方法简便。本文介绍一些常用三角代换及其在代数上的应用。 1若|a|≤1,联系到|sina|≤1,|cosa|≤1可作代换a=sina或a=cosa。例1 已知|a|<1,|b|<1,求证 |ab±((1-a~2)(1-b~2))~(1/2)|≤1。证明因为|a|<1,|b|<1,所以可令 In many algebraic problems, the corresponding trigonometric functions are introduced according to the range of values ​​of the relevant letters or satisfied conditions, and the use of trigonometric methods to solve these problems is often simpler than the pure algebraic method. This article describes some common trigonometric substitutions and their applications in algebra. 1 If |a|≤1, contact |sina|≤1,|cosa|≤1 may substitute a=sina or a=cosa. Example 1 It is known that |a|<1,|b|<1, to verify |ab±((1-a~2)(1-b~2))~(1/2)|≤1. Prove that because |a|<1,|b|<1, it can be made