tanαtan2α/(tan2α+tanα)=sin2α

题目

tanαtan2α/(tan2α+tanα)=sin2α
证明
tanatan2a/(tan2a-tana)+根号3(sin^2a-co^2)=2sin(2a-派/3) 证明下

答案

tanαtan2α/(tan2α+tanα)
=(sinasin2a/cosacos2a)/(sin2a/cos2a+sina/cosa)
=sinasin2a/(sin2acosa+cos2asina)
=sinasin2a/sin3a
=sin2a/(3-4sin^2a)