已知sin(2x+y)=5siny,(y不等于K派),求证;3tan=2tan(x+y)

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已知sin(2x+y)=5siny,(y不等于K派),求证;3tan=2tan(x+y)
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已知sin(2x+y)=5siny,(y不等于K派),求证;3tan=2tan(x+y)
已知sin(2x+y)=5siny,(y不等于K派),求证;3tan=2tan(x+y)

已知sin(2x+y)=5siny,(y不等于K派),求证;3tan=2tan(x+y)
sin[(x+y)+x]=5sin[(x+y)-x]
sin(x+y)·cosx+cos(x+y)·sinx=5·sin(x+y)·cosx-5·cos(x+y)·sinx
4·sin(x+y)·cosx=6·cos(x+y)·sinx
两边同除以cos(x+y)·cosx得:2·tan(x+y)=3·tanx