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一、三角函数方程化思想主要是指将所求解的函数之间的抽象关系转化成具体方程的方式进行解答的一种思想方法,体现在其证明、求值上面,如下面例题:例一:在△ABC中,内角A、B、C的对边分别为a、b、c,其中c=2,C=π/3。若sinC+sin(B-A)=2sin2A,求△ABC的面积。解题思路及过程:由题意只知道c边与C角的值,因此需要根据给出的三角函数公式,进行公式的转换。由题意可得:sin(B+A)+sin(B-A)=4sinAcosA,即得到sinBcosA=2sinAcosA
First, the trigonometric function of the idea of the main idea is to solve the abstract relationship between the functions to solve the specific equation to solve a way of thinking, reflected in its proof, the above evaluation, such as the following example: Example 1: In △ABC, the opposite sides of the inner corners A, B, and C are a, b, and c, respectively, where c=2 and C=π/3. If sinC+sin(B-A)=2sin2A, find the area of △ABC. Problem-solving ideas and process: Only the values of c-side and C-angle are known from the question. Therefore, the formula needs to be converted according to the formula of the given trigonometric function. The meaning of the question is: sin(B+A)+sin(B-A)=4sinAcosA, ie get sinBcosA=2sinAcosA