求证sinx+siny=2sin(x+y)/2*cos(x-y)/2
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sinx+siny
=sin[(x+y)/2+(x-y)/2]+sin[(x+y)/2-(x-y)/2]
=sin(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
=2sin(x+y)/2*cos(x-y)/2
其中第2项和第4项互为相反数
=sin[(x+y)/2+(x-y)/2]+sin[(x+y)/2-(x-y)/2]
=sin(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
=2sin(x+y)/2*cos(x-y)/2
其中第2项和第4项互为相反数
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