已知3cos(2x+y)+5cosy=0,则tan(x+y)tanx的值是线上等!

问题描述:

已知3cos(2x+y)+5cosy=0,则tan(x+y)tanx的值是
线上等!

cos(2x+y)=cos[(x+y)+x]=cos(x+y)cosx-sin(x+y)sinxcosy=cos[(x+y)-x]=cos(x+y)cosx+sin(x+y)sinx3cos(2x+y)+5cosy=8cos(x+y)cosx+2sin(x+y)sinx=0tan(x+y)tanx=-4