求证：（sin2x)(1+tanx*tan(x/2))/2cosx=tanx

图片上后面少打了个 =tan x

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由芹念腊倍角公式及半角公式高纳有：
sin(2x)=2sin(x)cos(x)
tan(x/2)=(1-cos(x))/嫌滑sin(x)

则，原式 = [2sin(x)cos(x)/2cos(x)]*{1+[sin(x)/cox(x)]*[(1-cos(x))/sin(x)]} = sin(x)*(1+(1-cos(x))/cos(x)) = sin(x)/cos(x) = tan(x)

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