已知tan(a+b)=1/5,tan(b+π/4)=1/4,求tana的值

题目

已知tan(a+b)=1/5,tan(b+π/4)=1/4,求tana的值

答案

tan(b+π/4)=1/4
[tanb+tan(π/4)]/[1-tanbtan(π/4)]=1/4
(tanb +1)/(1-tanb)=1/4
5tanb=-3
tanb=-3/5
tan(a+b)=1/5
(tana+tanb)/(1-tanatanb)=1/5
(tana -3/5)/[1+(3/5)tana]=1/5
(22/5)tana=4
tana=10/11