A B 为锐角tan(A-B)=sin(2B),求证2tan(2B)=tanA+tanB
问题描述：
A B 为锐角tan(A-B)=sin(2B),求证2tan(2B)=tanA+tanB
答
tan(A-B) = (tanA-tanB)/(1+tanAtanB) =sin(2B)=2sinBcosBtanA-tanB=2sinBcosB(1+tanAtanB)= 2sinBcosB+2tanAsin²BtanA(1-2sin²B)= 2sinBcosB+tanBtanA=(2sinBcosB+tanB)/cos(2B)tanA+tanB={sin(2B)+tanB[...