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在条件不等式的证明中,若已知条件为a>0,b>O且a+6=1或者a>O,b>O,c>O且a+b+c=1时,可引进三角函数建立相应的三角式后再给以证明。由于三角函数的公式较多,三角变换的规律相对说来容易遵循,故证明过程比较自然。在证明过程中,要根据三角函数的定义进行代数式与三角式的相互代换,还要结合一些基本不等式。因此,运用三角方法证明不等式,有利于开拓学生的证题思路,加强数学各科间的横向联系。下面通过一些例题介绍此种证法。
In the proof of conditional inequality, if the known conditions are a>0, b>O and a+6=1 or a>O, b>O, c>O, and a+b+c=1, triangles can be introduced. The function establishes the corresponding triangle and then gives proof. Because there are many formulas for trigonometric functions, the law of triangular transformation is relatively easy to follow, so the proof process is more natural. In the process of proof, algebraic and trigonometric substitutions are performed according to the definition of trigonometric functions, and some basic inequalities are also combined. Therefore, the use of the trigonometric method to prove inequality is conducive to the development of students’ ideas and strengthen the horizontal relationship between mathematics. Here are some examples to introduce this type of proof.