现行高中《代数》课本(甲种本)第一册第三章一开始就通过作辅助角-β,构造出两个全等的三角形ΔOP_1P_1与ΔOP_2P_4,然后利用等式|P_1P_3|=|P_2P_4(如图1),首先证明了两角和的余弦公式 cos(α+β)=cosαcosβ-sinaαsianβ.(C_+)其次,用-β代替β,导出了两角差的余弦公式 cos(α-β)=cosαcosβ+sinaαsinaβ (C_-) The third chapter of the current high school “Algebra” textbook (A type) of the first volume of the first chapter by the auxiliary angle -β, to construct two congruent triangles ΔOP_1P_1 and ΔOP_2P_4, and then use the equation | P_1P_3 | = | P_2P_4 ( As shown in Figure 1), the cosine of the two-cornered sum is firstly proved to be cos(α+β)=cosαcosβ-sinaαsianβ.(C_+). Then, β is used instead of β to derive the cosine of the two-corner cosine formula (α-β). )=cosαcosβ+sinaαsinaβ (C_-)