化简(1+sina-cosa)/ (1+sina+cosa)+(cosa/2)/(sina/2)

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化简(1+sina-cosa)/ (1+sina+cosa)+(cosa/2)/(sina/2)

化简(1+sina-cosa)/ (1+sina+cosa)+(cosa/2)/(sina/2)
化简(1+sina-cosa)/ (1+sina+cosa)+(cosa/2)/(sina/2)

化简(1+sina-cosa)/ (1+sina+cosa)+(cosa/2)/(sina/2)
1+sina-cosa=sina+(1-cosa)=2sin(a/2)cos(a/2)+2sin²(a/2)=2sin(a/2)[sin(a/2)+cos(a/2)]
1+sina+cosa=sina+(1+cosa)=2sin(a/2)cos(a/2)+2cos²(a/2)=2cos(a/2)[sin(a/2)+cos(a/2)]
所以原式=2sin(a/2)[sin(a/2)+cos(a/2)]/2cos(a/2)[sin(a/2)+cos(a/2)]+cos(a/2)/sin(a/2)
=sin(a/2)/cos(a/2)+cos(a/2)/sin(a/2)
=[sin²(a/2)+cos²(a/2)]/sin(a/2)cos(a/2)
=1/(1/2*sina)
=2/sina
=2csca