Temos que $$w = \frac{1+z}{1-z} = \frac{1+\cos{t} + i\sin{t}}{1-\cos{t}-i\sin{t}}$$ lembrando da famosa expressão do arco duplo: $$\cos{2x} = 2\cos^2{x}-1 = 1-2\sin^2{x} $$ $$=> w = \frac{1+2\cos^2{t/2}-1+i\sin{t}}{1-1+2\sin^2{t/2}-i\sin{t}} = \frac{2\cos^2{t/2}+i\sin{t}}{2\sin^2{t/2}-i\sin{t}}$$ Temos também, que $$\sin{t} = 2\sin{(t/2)}\cos{(t/2)}$$ substituindo, e fatorando o denominador e o numerador, $$w = \frac{\cos{t/2}}{\sin{t/2}} \cdot \frac{\cos{t/2}+i\sin{t/2}}{\sin{t/2}-i\cos{t/2}} = \frac{\cos{t/2}}{\sin{t/2}} \frac{(\cos{t/2}+i\sin{t/2})(\sin{t/2}+i\cos{t/2})}{(\sin{t/2}-i\cos{t/2})(\sin{t/2}+i\cos{t/2})}$$ $$=>w = \frac{\cos{t/2}}{\sin{t/2}} \frac{1 \cdot i}{1} = i \cot{\frac{t}{2}} => Letra \ A$$