
8. Kompleksan broj [inlmath]\frac{\cos\alpha+i\sin\alpha+1}{\cos\alpha+i\sin\alpha-1}\;\left(i=\sqrt{-1},\:\alpha\ne 2k\pi,\:k\in\mathbb{Z}\right)[/inlmath], jednak je:
[inlmath]\enclose{box}{\left(A\right)\;-i\cdot\mathrm{ctg}\frac{\alpha}{2}}\quad[/inlmath] [inlmath]\left(B\right)\;-i\cdot\frac{2\sin\alpha}{1-\cos\alpha}\quad[/inlmath] [inlmath]\left(C\right)\;-i\cdot\frac{2\sin\alpha}{2-\cos\alpha}\quad[/inlmath] [inlmath]\left(D\right)\;-i\cdot\frac{\sin\alpha}{2\left(1-\cos\alpha\right)}\quad[/inlmath] [inlmath]\left(E\right)\;-i\cdot\mathrm{tg}\frac{\alpha}{2}\quad[/inlmath] [inlmath]\left(N\right)\;\mbox{Ne znam}[/inlmath]