Question

Como fazer está resolução .

Answer 1

Explicação passo-a-passo:

$\cos(\frac{3\pi}{2}-\alpha)=\cos(\frac{3\pi}{2})\cos(\alpha)+sen(\frac{3\pi}{2})sen(\alpha)=-sen (\alpha) \therefore sen(\alpha)=\frac{4}{5}\\ \cos(\alpha)^2=1-sen(\alpha)^2=1-\frac{16}{25}=\frac{9}{25}\therefore \cos(\alpha)=\frac{3}{5}, \; \alpha \in \ ]0, \frac{\pi}{2}[ \\ tg(\alpha)=\frac{sen(\alpha)}{\cos(\alpha)}=\frac{\frac{4}{5}}{\frac{3}{5}}=\frac{4}{3} \\ \therefore 3-\frac{1}{tg(\alpha)}=3- \frac{1}{\frac{4}{3}}=3-\frac{3}{4}=\frac{12-3}{4}=\frac{9}{4}$