多倍角三角函数展开式的一组有趣的性质

Interesting Nature of the Expansions of Multiple-angle Trigonometric Functions

笔者发现同类的奇倍角三角函数展开式形式上具有异常的相似性。本文中对此给出严格的数学证明,并通过几道数学问题说明了此性质的应用方法。

The author finds that there is great similarity in the expansions of multiple-angle trigonometric functions.In this thesis,strict mathematical proof is given to this nature,and at the time,the application of the nature is demonstrated through a few mathematical problems.