在中等学校里是否需要证明三角不等式呢?我们认为是需要的,因为不等式的证明,即使是最简单的不等式的证明,也要求学生们去作讨论,并且应用不是千篇一律的方法,它能推动学生创造性的思维。实际上,就是最简单的例题:比较量cos40°和cos60°,也需要有自觉地应用三角函数的性质的本领。三角不等式的证明能培养学生以批判的态度来对待公式的结果,能使他们习惯于小心地进行推理。现在让我们来举一个实际例子。学生们常能毫无困难地推导出来大家熟知的公式 Is it necessary to prove triangular inequalities in secondary schools? We think it is necessary, because the proof of inequality, even the proof of the simplest inequality, requires students to discuss, and the application is not a one-size-fits-all approach, it can promote students Creative thinking. In fact, it is the simplest example: comparing the quantities cos40 and cos60, there is also a need to consciously apply the nature of trigonometric functions. The proof of the triangular inequality can cultivate the students’ results of treating the formula with a critical attitude, making them accustomed to careful reasoning. Let us now give a practical example. Students can often deduce well-known formulas without difficulty