求证:sin(2x+y)/sinx-2cos(x+y)=siny/sinx(2)已知5siny=sin(2x+y),求证:tan(x+y)=3/2 tanx

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/06 06:22:15

求证:sin(2x+y)/sinx-2cos(x+y)=siny/sinx(2)已知5siny=sin(2x+y),求证:tan(x+y)=3/2 tanx
求证:sin(2x+y)/sinx-2cos(x+y)=siny/sinx
(2)已知5siny=sin(2x+y),求证:tan(x+y)=3/2 tanx

求证:sin(2x+y)/sinx-2cos(x+y)=siny/sinx(2)已知5siny=sin(2x+y),求证:tan(x+y)=3/2 tanx
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