已知sinx+siny=2sin(x+y)≠0,则tanx/2tany/2等于 是三角函数和差化积部分的
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已知sinx+siny=2sin(x+y)≠0,则tanx/2tany/2等于 是三角函数和差化积部分的
![已知sinx+siny=2sin(x+y)≠0,则tanx/2tany/2等于 是三角函数和差化积部分的](/uploads/image/z/4685644-28-4.jpg?t=%E5%B7%B2%E7%9F%A5sinx%2Bsiny%3D2sin%28x%2By%29%E2%89%A00%2C%E5%88%99tanx%EF%BC%8F2tany%EF%BC%8F2%E7%AD%89%E4%BA%8E+%E6%98%AF%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0%E5%92%8C%E5%B7%AE%E5%8C%96%E7%A7%AF%E9%83%A8%E5%88%86%E7%9A%84)
sinx+siny=2sin(x+y)
2sin(x/2+y/2)cos(x/2-y/2)=4sin(x/2+y/2)cos(x/2+y/2)
cos(x/2-y/2)=2cos(x/2+y/2)
cos(x/2)cos(y/2)+sin(x/2)sin(y/2)=2cos(x/2)cos(y/2)-2sin(x/2)sin(y/2)
3sin(x/2)sin(y/2)=cos(x/2)cos(y/2)
tan(x/2)tan(y/2)=1/3
2sin(x/2+y/2)cos(x/2-y/2)=4sin(x/2+y/2)cos(x/2+y/2)
cos(x/2-y/2)=2cos(x/2+y/2)
cos(x/2)cos(y/2)+sin(x/2)sin(y/2)=2cos(x/2)cos(y/2)-2sin(x/2)sin(y/2)
3sin(x/2)sin(y/2)=cos(x/2)cos(y/2)
tan(x/2)tan(y/2)=1/3
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