高中《代数》第一册通过作辅助角-β,然后根据两个三角形全等和两点间距离公式证明了公式Cα+β,方法较繁,现给一种简捷法。证明建系如图5,作单位圆O,α、β角的始边为ox,交圆O于P,终边分别交圆O于P_1和P_2,其坐标是:P_1(cosα,sinα)P_2(cosβ,sinβ)。由余弦定理得 The first volume of “Algebra” in high school is used as the assistant angle -β, and then the formula Cα+β is proved according to the two triangles congruence and the distance formula between two points. The method is more complicated and a simple method is now given. Prove that the building is shown in Figure 5, for the unit circle O, the beginning of the α, β angle is ox, the intersection circle is O to P, and the end side intersects the circle O to P_1 and P_2 respectively. Its coordinates are: P_1(cosα,sinα)P_2 (cosβ, sinβ). Cosine Theorem