令SINa=t,COSa=u 则左边=2-2t+2u-2tu=1+1-2t+2u-2tu=t^2+u^2-2t+2u-2tu+1 右边=1-2t+2u+t^2+u^2-2tu 左边=右边 所以等式成立~ 因为直接用正弦、余弦打出来又容易混，角度又是a，结果正弦就变成了sina（新浪），侵权了~所以就用换元，写练习的时候第一步就不要写下去啦，直接用正弦余弦去写吧~
证：2(1-sina)(1+cosa) =2(1-sina+cosa-sinacosa) =1+1-2sina+2cosa-2sinacosa =[(sina)^2+(cosa)^2]+1-2sina+2cosa-2sinacosa =[1-2sina+(sina)^2]+2cosa-2sinacosa+(cosa)^2 =(1-sina)^2+2cosa(1-sina)+(cosa)^2 =(1-sina+cosa)^2=右边 证完
1-sinA =[sin(A/2)]^2+[cos(A/2)]^2 -2*sin(A/2)*cos(A/2)
=[sin(A/2)-cos(A/2)]^2
cosA =2*[cos(A/2)]^2 -1 =[cos(A/2)]^2 -[sin(A/2)]^2
==> 2(1-sinA)(1+cosA)
= 4*[sin(A/2)-cos(A/2)]^2*[cos(A/2)]^2 ...(1)
==> (1-sinA+cosA)^2
={[sin(A/2)-cos(A/2)]^2 +[cos(A/2)]^2 -[sin(A/2)]^2}^2
= 4*[sin(A/2)-cos(A/2)]^2*[cos(A/2)]^2 ...(2)
(1)(2) ==> 2(1-sinA)(1+cosA) =(1-sinA+cosA)^2
答：详情>>
