若A-B=π/6,tanA-tanB=2√3/3,求tanAtanB=

问题描述:

若A-B=π/6,tanA-tanB=2√3/3,求tanAtanB=

tan(A-B)=(tanA-tanB)/[1+tanAtanB]=√3/3
2√3/3/[1+tanAtanB]=√3/3
2/[1+tanAtanB]=1
1+tanAtanB=2
tanAtanB=1