已知a和b均为锐角,cosa=4/5,tan(a-b)=-1/3,则tanb等于多少
问题描述：
已知a和b均为锐角,cosa=4/5,tan(a-b)=-1/3,则tanb等于多少
答
a和b均为锐角，cosa=4/5
sina=根号(1-cos²a)=3/5
tana=sina/cosa=3/4
tan(a-b)=-1/3
(tana-tanb)/(1+tanatanb)=-1/3
3(3/4-tanb)=-1-3tanb/4
9-12tanb=-4-3tanb
9tanb=13
tanb=13/9
答
cosa=4/5
tana=3/4
tan(a-b)=-1/3
tanb=tan[a-(a-b)]
=[tana-tan(a-b)]/[1+tanatan(a-b)]
=[3/4+1/3]/(1-1/4)
=(13/12)/(3/4)
=13/9