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如所周知,同一个三角方程,用不同的方法去解,其解集的表达形式往往不同。对于这种情况,学生常感到迷惑不解。他们根据以往解方程的经验相信,只要解法正确,即使解法千差万别,答案总是相同的,唯一的。为什么解三角方程,竟会出现不同形式的答案?难道一个方程的解会有两个或两个以上的答案吗? 其实,答案的不同只是表现在形式上,答案在实质上是唯一的。这里,形式的相异性掩盖了实质的唯一性。为了给学生讲清这一点,已有不少文章对之进
As is well known, the same triangular equation is solved by different methods, and the solution sets often have different expression forms. Students often feel puzzled about this situation. Based on previous experience with solving equations, they believe that as long as the solution is correct, even if the solution is very different, the answer is always the same and unique. Why solve the triangular equation, there will be different forms of answers? Is there an answer to the equation will have two or more answers? In fact, the difference in the answer is only in the form of the answer, the answer is essentially unique. Here, the dissimilarity of the form masks the uniqueness of the substance. In order to clarify this point for students, many articles have been written about it.