若cos(a+b)=1/5.cos(a-b)=3/5,则tana*tanb=?

题目

若cos(a+b)=1/5.cos(a-b)=3/5,则tana*tanb=?

答案

cos(a+b)=cosa*cosb-sina*sinb=1/5①
cos(a-b)=cona*conb+sina*sinb=3/5②
①＋②：cosa*cosb=2/5
②-①:sina*sinb=1/5
tana*tanb=(sina*sinb)/(cosa*coab)=1/2