若cos(a+b)=4/5 cos(a-b)=-3/5 则tana*tanb=?

题目

若cos(a+b)=4/5 cos(a-b)=-3/5 则tana*tanb=?
RT

答案

cosacosb-sinasinb=4/5
cosacosb+sinasinb=-3/5
sinasinb=(-3/5-4/5)/2=-7/10
cosacosb=(4/5-3/5)/2=1/10
tana*tanb=(sinasinb)/(cosacosb)=-7/10/(1/10)=-7