设tan(A/2)=t
则cosA=(1-t^2)/(1+t^2)
sinA=2t/(1+t^2)
则原式为
(1-t^2)/[2(1+t^2)-2t]:(1+t^2-2t)/(1-t^2)
(1-t^2)/[2(1+t^2)-2t]:(1-t)/(1+t)
(1+t)^2:2(t^2-t+1)
将t=tan(A/2)代回,用到公式[sec(A/2)]^2=[tan(A/2)]^2+1
[1+2sin(A/2)cos(A/2)]/[cos(A/2)]^2 :[2-2sin(A/2)cos(A/2)]/[cos(A/2)]^2
1+sinA:2-sinA