若tan(2x-y)=3tan(x-2y)=3,则tan(x+y)=

题目

若tan(2x-y)=3tan(x-2y)=3,则tan(x+y)=

答案

tan(x+y)=tan[(2x-y)+（x-2y）]=[tan(2x-y)+tan(x-2y)]/[1-tan(x-2y)*tan(2x-y)]
=(3+1)/(1-3*1)=-2