求证tan(a/2)-1/(tana/2)=-2/tana

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求证tan(a/2)-1/(tana/2)=-2/tana
求证tan(a/2)-1/(tana/2)=-2/tana

求证tan(a/2)-1/(tana/2)=-2/tana
tan(a/2)-1/(tana/2)
=sin(a/2)/cos(a/2)-cos(a/2)/sin(a/2)
通分
=[sin²(a)-cos²(a/2)]/[sin(a/2)cos(a/2)]
=-cosa/[(sina)/2]
=-2cosa/sina
=-2/tana
证毕

tan(a/2)-1/(tana/2)
=sin(a/2)/cos(a/2)-cos(a/2)/sin(a/2)
=[sin²(a)-cos²(a/2)]/[sin(a/2)cos(a/2)]
=-cosa/[(sina)/2]
=-2cosa/sina
=-2/tana