浅谈角的等式的证明及其教学

• 作 者: 潘正矩
• 机 构: 江苏高淳县永丰中学,
• 出 处: 中学数学
• 发表日期: 1988年12期
• 关键词: 证明题 单调区间 值相等 证法 推证 过山 多对一 处理方法 法时

在三角部分,常遇到两边都是角的恒等式或条件等式的证明题.对于这类题目,采用从一边到另一边之类的常规证法都难以奏效,一般常采用这样的证法:要证得α=β,先证得α、β的同名函数值相等,即 f(α)=f(β),再进一步证得α=β.学生证这类题,第一个步骤的困难不会太大,但第二步由 f(a)=f(β)推出α=β则常常出现困难和错误.

In the triangle part, it is often encountered that both sides are angular identities or proofs of conditional equations. For such topics, it is difficult to use conventional proofs such as from side to side, and generally such proofs are often used: To prove that α=β, first verify that the functions of the same name of α and β are equal, that is, f(α)=f(β), and further prove that α=β. Problems such as student cards, difficulties in the first step Not too large, but the second step from the f (a) = f (β) introduced α = β is often difficult and wrong.