已知sin(2x+y)=5siny,(y不等于K派),求证;3tan=2tan(x+y)

来源:学生作业学帮网 编辑:学帮网 时间:2024/05/15 05:27:18

已知sin(2x+y)=5siny,(y不等于K派),求证;3tan=2tan(x+y)

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