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数学竞赛中的许多代数问题,结构复杂,变元较多,学生往往陷入盘根错节的变量关系之中难以理清头绪,找不到解题切入点而无从下手,这时如果我们借助题目显现的某些特征和关系,从分析问题的整体结构出发,类比联想相关三角公式和恒等式模型,适时采用三角换元,不仅能简化题设信息,使隐性条件显性化,而且可以沟通变元之间的关系,使繁杂的代数问题转化为简单的三角
Many algebraic problems in the mathematics competition are complex in structure, with many variables, and students often fall into the intertwined relationship of variables and find it difficult to sort out the clues. If there is no solution point and no starting point, if we use the topic to show a certain These characteristics and relationships, starting from the overall structure of the analysis problem, analogy with the associated trigonometric formulas and identity models, and the timely adoption of triangular substitutions not only simplify the title setting information, make implicit conditions explicit, but also communicate between arguments. Relationships, transform complicated algebra problems into simple triangles