数学问题cot(x/2)=cosx/(1-sinx)是不是正确的,有推导过程最好

Question

数学问题
cot(x/2)=cosx/(1-sinx)是不是正确的,有推导过程最好

Answer 1

不对
cot(x/2)
=cos(x/2)/sin(x/2)
=2cos²(x/2)/[2sin(x/2)cos(x/2)]
=(1+cosx)/sinx
或者
cot(x/2)
=cos(x/2)/sin(x/2)
=2sin(x/2)cos(x/2)/[2sin²(x/2)]
=sinx/(1-cosx)