If z=eiθz = e^{i\theta}z=eiθ, which of the following is equivalent to 11−z\frac{1}{1-z}1−z1?
12+i2cot(θ2)\frac{1}{2} + \frac{i}{2} \cot(\frac{\theta}{2})21+2icot(2θ)
12−i2cot(θ2)\frac{1}{2} - \frac{i}{2} \cot(\frac{\theta}{2})21−2icot(2θ)
cos(θ)+isin(θ)\cos(\theta) + i\sin(\theta)cos(θ)+isin(θ)
12+icot(θ)\frac{1}{2} + i\cot(\theta)21+icot(θ)