化简sin(x+y)sinx+cos(x+y)cosx等于?

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化简sin(x+y)sinx+cos(x+y)cosx等于?
化简sin(x+y)sinx+cos(x+y)cosx等于?

化简sin(x+y)sinx+cos(x+y)cosx等于?
sin(x+y)sinx+cos(x+y)cosx=
(sinxcosy+sinycosx)sinx+(cosxcosy-sinxsiny)cosx=
(sinx)^2 *cosy+(cosx)^2*cosy=
(sinx平方+cosx平方)*cosy=
1*cosy=cosy

由cos(x-y)=cosxcosy+sinxsiny
有:sin(x+y)sinx+cos(x+y)cosx
=cos[(x+y)-x]
=cosy

sin(x+y)sinx+cos(x+y)cosx=(sinxcosy+cosxsiny)sinx+(cosxcosy-sinxsiny)cosx=sinxsinxcosy+sinxcosxsiny+cosxcosxcosy-sinxcosxsiny=(sinxsinx+cosxcosx)cosy=cosy

(sinXcosY+cosXsinY)*sinX+(cosXcosY-sinXsinY)*cosX
=(sinX^2+cosX^2)*cosY+(cosXsinX-cosXsinX)*sinY
=cosY