3cosx-sinx=2sinx=3cosx-2(sinx)^2+(cosx)^2=10(cosx)^2-12cosx+4=110(cosx)^2-12cosx+3=0(cosx-3/5)^2=3/50cosx=(3+2√6)/5(>1,舍去)或cosx=(3-2√6)/5x=arccos[(3-2√6)/5]