求证:sin(2x+y)/sinx-2cos(x+y)=siny/sinx
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![求证:sin(2x+y)/sinx-2cos(x+y)=siny/sinx](/uploads/image/z/351073-1-3.jpg?t=%E6%B1%82%E8%AF%81%EF%BC%9Asin%282x%2By%29%2Fsinx-2cos%28x%2By%29%3Dsiny%2Fsinx)
求证:sin(2x+y)/sinx-2cos(x+y)=siny/sinx
求证:sin(2x+y)/sinx-2cos(x+y)=siny/sinx
求证:sin(2x+y)/sinx-2cos(x+y)=siny/sinx
证:
sin(2x+y)/sinx -2cos(x+y)
=[ sin[(x+y)+x] -2cos(x+y)sinx ]/sinx
=[sin(x+y)cosx+cos(x+y)sinx-2cos(x+y)sinx]/sinx
=[sin(x+y)cosx-cos(x+y)sinx]/sinx
=sin[(x+y)-x]/sinx
=siny/sinx
等式成立.
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证明 [sin(2x+y)/sinx]-2cos(x+y)=siny/sinx