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

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

人气：427 ℃　时间：2020-04-02 20:08:51

解答

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