cos(a+b)=cosacosb-sonasinb=1/3
cos(a-b)=cosacosb+sonasinb=1/2
相加,2cosacosb=5/6
cosacosb=5/12
所以sinasinb=1/12
tanatanb=sinasinb/cosacosb=1/5
所以原式=log5(1/5)
=log5(5^(-1))
=-1*log5(5)
=-1