cos(a-b)cos(b-c)+sin(a-b)sin(b-c)=

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cos(a-b)cos(b-c)+sin(a-b)sin(b-c)=

cos(a-b)cos(b-c)+sin(a-b)sin(b-c)=
cos(a-b)cos(b-c)+sin(a-b)sin(b-c)=

cos(a-b)cos(b-c)+sin(a-b)sin(b-c)=
cos(a-b)cos(b-c)+sin(a-b)sin(b-c)
=cos[(a-b)-(b-c)]
=cos(a+c-2b)

利用和差角公式cos(x-y)=cosxcosy+sinxsiny
式中的a-b相当于x,b-c相当于y
所以原式=cos[(a-b)-(b-c)]=cos(a+c-2b)

cos(a+c-2b)

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