对含有某角的三角函数的偶次幂的三角函数式,通过“换元、降次”,将其转化为代数式来求解,往往使得解题简捷。反过来,有的数学问题,通过三角换元后,化为三角函数式问题来处理,这种方法,叫做三角换元法。三角换元法是高等数学中的一种重要方法,在初等数学中也有着较广泛的应用。有的问题应用三角换元法去解,不仅可化难为易,使得解题简便,而且能让学生养成“一题多解”的习惯,开扩视野,发展思维,加深对函数概念和等价变换更加探入的理解。现从以下几个方面举例说明。 For a trigonometric function of an even power of a trigonometric function containing a certain angle, it is converted into an algebraic expression by “transition, degeneracy,” to solve the problem, which often makes the solution simple and easy. In turn, some mathematical problems are dealt with by trigonometric transformations, which are treated as trigonometric functions. This method is called the triangle-changing method. Triangular substitution method is an important method in higher mathematics. It also has a wider application in elementary mathematics. Some problems are solved by the triangle-changing method, which can not only make it difficult to make things easier, but also make it easier to solve problems. It also allows students to develop the habit of “multiple solutions to one problem”, expand their horizons, develop their thinking, deepen the concept of functions, etc. The price change is more insightful to the understanding. Here is an example from the following aspects.