问题标题：
X-Y=（2π）／3,cosX+cosY=1／3求cos(X+Y)=?
问题描述：
X-Y=（2π）／3,cosX+cosY=1／3求cos(X+Y)=?
马西奎回答：
和差化积
cosX+cosY=cos[(X+Y)/2+(X-Y)/2]+cos[(X+Y)/2-(X-Y)/2]
=cos[(X+Y)/2]cos[(X-Y)/2]-sin[(X+Y)/2]sin[(X-Y)/2]+cos[(X+Y)/2]cos[(X-Y)/2]+sin[(X+Y)/2]sin[(X-Y)/2]
=2cos[(X+Y)/2]cos[(X-Y)/2]
=2cos[(X+Y)/2]cosπ/3
=cos[(X+Y)/2]=1/3
故cos(X+Y)=2cos²[(X+Y)/2]-1=2*(1/3)²-1=-7/9
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