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三角等式证明,不仅涉及的知识面广,而且有一定的灵活性和较高的技巧性,学生往往感到困难。如何帮助学生开拓思路,提高分析问题和解决问题的能力,大家都在摸索、尝试。三角题中条件和结论问的差异主要表现在三角函数式上,也就是三角函数式的名称和三角函数的角这两个方面的差异。在备课时如能紧扣主题,归类分析、抓牢一点,启发诱导,让学生在解题时心中有条路子,眼前有个方向,那么,教与学就能收到成效。在“三角等式证明”一堂习题课中,我紧紧抓住上述两大差异,启发学生思考,帮助他们定向,探索三角等式证明的规律,收到了较好的效果。现介绍如下。例一已知 tg~2a=1+2tg~2β·求证cos~2β=1+cos~2a. 考察条件与结论间的差异。(1)角的差异是:2a
The triangular equation proves that not only the knowledge involved is wide, but also it has certain flexibility and high skill. Students often feel difficult. How to help students develop ideas and improve their ability to analyze and solve problems, everyone is exploring and trying. The differences between the conditions and conclusions in the trigonometric problem are mainly reflected in the trigonometric function, which is the difference between the name of the trigonometric function and the angle of the trigonometric function. If you can closely follow topics during class preparation, classify and analyze, grasp one thing, and inspire guidance, let students have a way to solve problems and have a direction in front of them. Then, teaching and learning can be effective. In the “Proof of Trigonometric Equations” class, I firmly grasped the above two differences, inspired students to think, help them to target, explore the laws of the trigonometric equations, and received good results. The introduction is as follows. Example 1 Known tg~2a=1+2tg~2β· Proof COS~2β=1+cos~2a. Examine the differences between conditions and conclusions. (1) The difference in angles is: 2a