已知:3sinY=sin(2X+Y),求证tan(X+Y)=2tanX

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已知:3sinY=sin(2X+Y),求证tan(X+Y)=2tanX已知:3sinY=sin(2X+Y),求证tan(X+Y)=2tanX已知:3sinY=sin(2X+Y),求证tan(X+Y)=

已知:3sinY=sin(2X+Y),求证tan(X+Y)=2tanX
已知:3sinY=sin(2X+Y),求证tan(X+Y)=2tanX

已知:3sinY=sin(2X+Y),求证tan(X+Y)=2tanX
令a=x+y,则条件变为
3sin(a-x)=sin(a+x),展开得
3sinacosx-3cosasinx=sinacosx+cosasinx,移项
2sinacosx=4cosasinx
tana=2tanx,于是
tan(x+y)=2tanx