用三角函数万能公式化简 y=（1-sinx）/（1+cosx）,得y=1/2×（tan a/2-1）^2,

就是用万能公式做的：
万能公式：sinx=2tan(x/2)/(1+tan(x/2)^2)
cosx=(1-tan(x/2)^2)/(1+tan(x/2)^2)
令：t=tan(x/2)
y=(1-2t/(1+t^2))/(1+(1-t^2)/(1+t^2))
=(t-1)^2/2
=(1/2)(tan(x/2)-1)^2
求导是一样的：
y=(1-sinx)/(1+cosx)
y'=(-cosx(1+cosx)+(1-sinx)sinx)/(1+cosx)^2
=(sinx-cosx-1)/(4cos(x/2)^4)
=(2sin(x/2)cos(x/2)-2cos(x/2)^2)/(4cos(x/2)^4)
=2cos(x/2)(sin(x/2)-cos(x/2))/(4cos(x/2)^4)
=(sin(x/2)-cos(x/2))/(2cos(x/2)^3)
y=(1/2)(tan(x/2)-1)^2
y'=(1/2)(2(tan(x/2)-1)sec(x/2)^2/2)
=(1/2)((tan(x/2)-1)/cos(x/2)^2
=(1/2)(sin(x/2)/cos(x/2)-1)/cos(x/2)^2
=(1/2)(sin(x/2)-cos(x/2))/cos(x/2)^3

请问，哪来的a/2？打错了，是x/2对的，不过好像不是用万能公式解的两边求导结果不一样，求完整求导过程

1年前