来自黄凤辰的问题
【已知tan(x+y)=3tanx,求证:2sin2y-sin2x=sin(2x+2y)】
已知tan(x+y)=3tanx,求证:2sin2y-sin2x=sin(2x+2y)
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2020-06-24 15:54
【已知tan(x+y)=3tanx,求证:2sin2y-sin2x=sin(2x+2y)】
已知tan(x+y)=3tanx,求证:2sin2y-sin2x=sin(2x+2y)
证明:要证2sin2y-sin2x=sin(2x+2y),即要证2sin2y=sin2x+sin(2x+2y)=2sin(2x+y)cosy(利用和差化积)即要证4sinycosy=2sin(2x+y)cosy两边消去2cosy,得2siny=sin(2x+y)也即要证2siny=sin2xcosy+sinycos2x,即siny(2-co...