已知8cos(2x+y)+5cosy=0,且x不等于kx+pi/2,x+y不等于kx+pi/2(k属于Z),求tan(x+y)tanx的值?
问题描述:
已知8cos(2x+y)+5cosy=0,且x不等于kx+pi/2,x+y不等于kx+pi/2(k属于Z),求tan(x+y)tanx的值?
答
8cos(2x+y)+5cosy=08cos(2x+y)=-5cosy8cos[(x+y)+x]=-5cos[(x+y)-x]8[cos(x+y)cosx-sin(x+y)sinx]=-5[cos(x+y)cosx+sin(x+y)sinx]8cos(x+y)cosx-8sin(x+y)sinx=-5cos(x+y)cosx-5sin(x+y)sinx13cos(x+y)cosx=3sin(x...