两角和与差的正、余弦公式常常被称为平面三角学的基本公式,这些公式随着三角学的诞生而诞生,有着十分悠久的历史.打开20世纪中叶以前的任何一部西方三角学著作,我们都能看到,这些公式中至少有一个是用几何方法推导证明的,不同作者在方法的选择上各有所爱,各种方法汇总起来,可谓精彩纷呈、蔚为大观,为我们今天的教材编写以及HPM视角下的公式教学提供了十分丰富的素材.1托勒密定理公元2世纪,古希腊天文学家托勒密(C. The positive and negative cosmos of the corners and corners are often referred to as the basic formulas of plane trigonometry, which were born with the birth of trigonometry and have a long history. Open any western trigonometry before the middle of the twentieth century Works, we can see that at least one of these formulas is proven by geometric methods, different authors each have their own love in the choice of method, a variety of methods can be described as brilliant, spectacular, as we are today Textbook compilation and formula teaching under the HPM perspective provides a very rich material.1 Ptolemy theorem The 2nd century AD, the ancient Greek astronomer Ptolemy (C.