反证法是一种電要的证明方法,它在数学的各个方面作用很大.下面仅就平面三角这部分内容,谈谈反证法的应用. 一、证明三角不等式例1 证明对于任何的x值,不等式1/3≤(tg3x)/(tgx)≤3 都不成立证明假定有某一个α,满足上面不等式,即有1/3≤(tg3α)/(tgα)≤3 (1)由正切的定义可知,这个α要满足下列条件α≠kπ (k为任意辂数)(2) The counter-evidence method is a kind of proof method for electricity. It plays a very important role in all aspects of mathematics. The following is only the application of counter-evidence in this part of the plane triangle. I. Prove that the triangle inequality Example 1 proves that for any value of x, inequality 1/3 ≤ (tg3x)/(tgx) ≤ 3 is not satisfied. It is proved that there is an α that satisfies the above inequality, that is, 1/3 ≤ (tg3α)/(tgα) ≤ 3 (1) is known from the definition of tangent. This α satisfies the following conditions α≠kπ (k is an arbitrary number of turns) (2)