(sina+cosa-1)(sina-cosa+1)/sin2a
=[sina²-(cosa-1)²]/sin2a
=(1-cos²a-cos²a+2cosa-1)/2sinacosa
=(2cosa-2cos²a)/2sinacosa
=(1-cosa)/sina
=2sin²(a/2)/2sin(a/2)cos(a/2)
=sin(a/2)/cos(a/2)
=tan(a/2)