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本文仅就用三角代换法解题过程中必须注意确定θ角范围的问题,谈谈笔者的浅见。我认为,在对题目中的未知数或自变量确定了具体的三角代换式,则θ角的取值范围也就由原题目本身确定下来了。认真地分析原题,仔细地确定好角θ的范围,是确保解题结果正确无误的一个重要环节。不注意θ角的取值范围,破坏了代换前后的取值统一,将会导致解题结果出现错误。下面举出数例具体地说明上述看法。例1 解方程x(4-x~2)~(1/2)=2/x~2-2 分析可设x=2cosθ;经观察知,如要方程等号的两侧均有意义,并且同时为正或为负
In this paper, we only need to pay attention to the problem of determining the range of θ angle in the process of solving problems with the triangle substitution method, and talk about the author’s superficial views. In my opinion, when a specific triangle substitution formula is determined for the unknown number or independent variable in the title, the range of values for the angle θ is determined by the original title itself. Careful analysis of the original question and careful determination of the range of angle θ are an important part of ensuring the correctness of the problem. Paying no attention to the range of values of the angle θ destroys the uniform values before and after the substitution, which will result in the wrong results. Here are some examples of concrete explanations of the above observations. Example 1 The solution equation x(4-x~2)~(1/2)=2/x~2-2 analysis can be set to x=2cosθ; it is observed that if both sides of the equation equal sign are significant, and At the same time positive or negative