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一、三角学中的恒等变換 我們知道,加法定理以及由加法定理推出的各种公式(指簡化公式,倍角半角公式,积化和差、和差化积公式等等)与基本三角恆等式是三角恆等变換的基础。这些恆等变換就其作法来說不尽相同,因而很难給出一般的法则,也很难預知各种能以簡化的因素。要作到合理变换,除必須依靠不断实践和树立頑强学习精神外,还必須相应地掌握一些解題的技能和技巧。下面就用倍角的正弦和余弦的代数和表示正弦和余弦的方冪公式(或簡称‘降冪公式’)以及积化和差等問題談談自己的一些体会: 1.关于用倍角的正弦
First, the identity transformation in trigonometry We know that the addition theorem and the various formulas introduced by the addition theorem (referring to the simplified formula, double-width half-angle formula, product and difference, and differential product formula, etc.) and the basic triangular identity It is the basis of the trigonometric transformation. These identity transformations are not the same for their practices, and it is difficult to give a general rule, and it is difficult to foresee various factors that can be simplified. In order to achieve a reasonable transformation, in addition to relying on continuous practice and establishing a tenacious spirit of learning, it is also necessary to acquire some skills and techniques for solving problems. Let’s talk about some of our experiences with algebraic expressions of the sine and cosine of the double angles and the powers of the formulas that represent the sine and cosine (or simply the “power down” formula) and the productization and difference: 1. About the sine with a double angle