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在高中内要傅授解三角方程式的知识时固然首先要求同学通晓那些恒等变换的公式,但是往往由于解方程的技巧的丰富多采而使同学颇难系统地掌握,即使教师有时解出了方程而不知为何用此法求解。事实上三角方程求解大多数要借助于技巧。例如解三角方程sin 2x sin 7x+sin 11xsin 20x+sin 17x sin 48x=0宜乎用積化差公式化簡得cos 5x-cos 65x=0,然后再施用差化積公式化简得sin 30x sin 35x=0从而得到它的解是x=(nπ)/15或(2nπ)/35,其中n是任意整数。
In high school, when you want to interpret the knowledge of the triangular equation, you first ask your classmates to be familiar with the formulas of the equivalence transformation. However, due to the rich variety of skills in solving the equations, the students are quite difficult to master systematically, even if the teacher sometimes solves them. The equation and I do not know why to use this method to solve. In fact, most of the trigonometric equations are solved by techniques. For example, the solution of the trigonometric equation sin 2x sin 7x + sin 11xsin 20x + sin 17x sin 48x = 0 is appropriate to formulate with the product difference simply cos 5x-cos 65x = 0, and then apply the difference product formulae simply sin 30x sin 35x = 0 thus gets its solution is x = (nπ)/15 or (2nπ)/35, where n is an arbitrary integer.