证明 [sin(2x+y)/sinx]-2cos(x+y)=siny/sinx
来源:百度知道 编辑:UC知道 时间:2024/09/26 10:51:36
[sin(2x+y)/sinx]-2cos(x+y)
={[sin(x+y)cosx+cos(x+y)sinx]/sinx}-2cos(x+y)
={[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
把5siny=sin(2x+y)变为5sin[(x+y)-x]=sin[(x+y)+x],把其中的(x+y),看成一个整体,上式即变为4sin(x+y)cosx=6cos(x+y)sinx,再把式子的左右两边变换为sin(x+y)/cos(x+y)=3/2sinx/cosx,即tan(x+y)=3/2 tanx
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