tan(a+b)=3/4,tan(a-π/4)=1/2,那么tan(b+π/4)等于多少

题目

tan(a+b)=3/4,tan(a-π/4)=1/2,那么tan(b+π/4)等于多少

答案

b+π/4=a+b-(a-π/4)
tan(b+π/4)
=tan{a+b-(a-π/4)}
={tan(a+b)-tan(a-π/4)}/{1+tan(a+b)tan(a-π/4)}
=(3/4-1/2)/(1+3/4*1/2)
=2/11