求证:sin(2x+y)/sinx-2cos(x+y)=siny/sinx

问题描述:

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.