若cos(α+β)=-3/5,cos(α-β)=12/13,则tanαtanβ=

问题描述:

若cos(α+β)=-3/5,cos(α-β)=12/13,则tanαtanβ=

cos(a-b)-cos(a+b)=2sinacosb=99/65
cos(a+b)+cos(a-b)=2cosacosb=21/65
所以
tanatanb=sinacosb/cosacosb=99/65*65/21=33/7