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两角差的余弦公式推导五种方法
更新时间: 2020-10-30 00:00:00  

两角差的余弦公式:cos(α-β)=cosαcosβ+sinαsinβ。可以用:向量法,两点间距离法,复数法,高斯公式法,几何法推导。

举例:复数推导法

(cosa+isina)(cos(-b)+isin(-b))=cos(a-b)+isin(a-b)

(cosa+isina)(cos(-b)+isin(-b))=(cosacosb+sinasinb)+i(sinacosb-cosasinb)

比较实部和虚部得:

cos(a-b)=cosacosb+sinasinb

sin(a-b)=sinacosb-cosasinb

关键词: 余弦 公式 推导 方法

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