(1+sina-cosa)^2+(1+cosa-sina)^2

(1+sina-cosa)^2+(1+cosa-sina)^2
=[1+(sina-cosa)]^2+[1+(cosa-sina)]^2
=1+2(sina-cosa)+(sina-cosa)^2+1+2(cosa-sina)+(cosa-sina)^2
=2+2(sina-cosa)^2
=2+2(sina^2+cosa^2-2sinacosa)
=2+2(1-2sinacosa)
=2+2(1-sin2a)
=2-2sin2a

(1+sina-cosa)^2+(1+cosa-sina)^2
=1+sina^2+cosa^2+2sina-2cosa-2sinacosa+1+cosa^2+sina^2+2cosa-2sina-2sinacosa
=4-4sinacosa
=4-2sin2a

原式=[1+（sina-cosa）^2+2*sina*cosa]+[1+(sina-cosa)^2-2*sina*cosa]
=2+2(sina-cosa）^2
=2+2*(1-2*sina*cosa)
=2+2-4*sina*cosa
=4-2*2*(sina*cosa)
=4-2sin2a

把sina-cosa 和 cosa-sina 分别看成一项，开平方，整理既得，OK
！