Question

已知tan(a+b)=1/5,tan(b+π/4)=1/4,求tana的值

Answer 1

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