It is given that $z=\cos\theta+i\sin\theta,\quad0\le\theta

Question

It is given that $z=\cos\theta+i\sin\theta,\quad0\le\theta<2\pi,\quad\theta\ne\pi.$ Show clearly that $\dfrac{2}{1+z}=1-i\tan(\theta/2).$

Accepted Answer

$\dfrac{2}{1+z}=1-i\tan(\theta/2)$ for $0\le\theta<2\pi,\ \theta\ne\pi$.

Complex Numbers Q1