A B 为锐角tan(A-B)=sin(2B),求证2tan(2B)=tanA+tanB_数学解答

A B 为锐角tan(A-B)=sin(2B),求证2tan(2B)=tanA+tanB

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解答

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[...