求证(tanxtan2x/tan2x-tanx)/(tan2x-tanx)+√3(sin^2x-cos^2x)=2sin(2x-π/3)

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求证(tanxtan2x/tan2x-tanx)/(tan2x-tanx)+√3(sin^2x-cos^2x)=2sin(2x-π/3)

求证(tanxtan2x/tan2x-tanx)/(tan2x-tanx)+√3(sin^2x-cos^2x)=2sin(2x-π/3)
求证(tanxtan2x/tan2x-tanx)/(tan2x-tanx)+√3(sin^2x-cos^2x)=2sin(2x-π/3)

求证(tanxtan2x/tan2x-tanx)/(tan2x-tanx)+√3(sin^2x-cos^2x)=2sin(2x-π/3)
tanxtan2x/(tan2x-tanx)
=sinxsin2x/(sin2xcosx-sinxcos2x)=sinxsin2x/sin(2x-x)=sin2x
(tanxtan2x/(tan2x-tanx))+√3[(sinx)^2-(cosx)^2]
=sin2x-√3cos2x
=2sin(2x-π/3)