已知tan(a+b)=1/3,tanb=1/4,则tana=

已知tan(a+b)=1/3,tanb=1/4,则tana=
已知tan(a+b)=1/3,tanb=1/4,则tana=

已知tan(a+b)=1/3,tanb=1/4,则tana=
tan(a+b)=1/3
(tana+tanb)/(1-tanatanb)=1/3
(tana+1/4)/(1-tana*1/4)=1/3
分子分母乘以4得
(1+4tana)/(4-tana)=1/3
1+4tana=(4-tana)*1/3
3+12tana=4-tana
13tana=1
tana=1/13

tan(a+b)
=(tana+tanb)/(1-tanatanb)=1/3
tanb=1/4
3tana+3/4=1-1/4tana
tana=1/13