三角函数sin(x-y)cosy+cos(x-y)siny化简要详细过程

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三角函数sin(x-y)cosy+cos(x-y)siny化简要详细过程

三角函数sin(x-y)cosy+cos(x-y)siny化简要详细过程
三角函数sin(x-y)cosy+cos(x-y)siny化简要详细过程

三角函数sin(x-y)cosy+cos(x-y)siny化简要详细过程
sin(x-y)cosy+cos(x-y)siny
=sin[(x-y)+y]
=sinx

解根据两角和差公式
sin(x-y)cosy+cos(x-y)siny
=sin[(x-y)+y]
=sinx

(sinxcosy-cosxsiny)cosy+(cosxcosy+sinxsiny)siny
=sinx(cosy)^2-cosxsinycosy+cosxsinycosy+sinx(siny)^2
=sinx[(cosy)^2+(siny)^2]
=sinx
望采纳O(∩_∩)O谢谢

cosα-cosβ=-2sin[(α β)/2]sin[(α-β)/2] 积化和差公式: 【注:(I)这步是利用

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