三角函数不仅是高中数学和继续学习数学、物理等学科的基础,也是一种解决数学问题的重要工具。在近几年的数学竞赛中,出现了不少以倍角公式为背景的优秀试题,旨在考查学生的联想思维能力和创新意识。根据二项定理和复数的棣莫佛定理,不难得到n(n∈N~*)倍角的正弦公式、余弦公式: Trigonometric functions are not only the basis of high school mathematics and continuing study of mathematics and physics, but also an important tool for solving mathematical problems. In recent years, mathematics competition, there have been many times the angle formula as the background of the outstanding questions, to examine the students’ thinking ability and sense of innovation. According to the binomial theorem and the plural Demov theorem, it is not hard to get the sine formula of n (n∈N ~ *) multiplier angle. The cosine formula is: