求解一道三角函数体已知sin(2x+y)=5siny,求证2tan(x+y)=3tanx.

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求解一道三角函数体已知sin(2x+y)=5siny,求证2tan(x+y)=3tanx.

求解一道三角函数体已知sin(2x+y)=5siny,求证2tan(x+y)=3tanx.
求解一道三角函数体
已知sin(2x+y)=5siny,求证2tan(x+y)=3tanx.

求解一道三角函数体已知sin(2x+y)=5siny,求证2tan(x+y)=3tanx.
别人提问是需要有详细解答过程的:
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