若a+b=π/6,则根号3(tanatanb-1)+3(tana+tanb)=
问题描述：
若a+b=π/6,则根号3(tanatanb-1)+3(tana+tanb)=
答
tan(a+b)=(tana+tanb)/(1-tanatanb)tan(π/6)=(tana+tanb)/(1-tanatanb)√3/3=(tana+tanb)/(1-tanatanb)√3(1-tanatanb)=3(tana+tanb)√3(tanatanb-1)+3(tana+tanb)=0