Question

Questões 7, 8 e 9 por favor

Answer 1

7)
$cos(x)=\sqrt{1-sen^2(x)}\\ cos(x)=\sqrt{1-(\frac{4}{5})^2}\\ cos(x)=\sqrt{1-\frac{16}{25}}\\ cos(x)=\sqrt{\frac{9}{25}}=\frac{3}{5}$

$tg(x)=\frac{sen(x)}{cos(x)}\\ tg(x)=\frac{\frac{4}{5}}{\frac{3}{5}}=\frac{4}{3}$

$sec(x)=\frac{1}{cos(x)}\\ sec(x)=\frac{1}{\frac{3}{5}}=\frac{5}{3}$

$cotg(x)=\frac{1}{tg(x)}\\ cotg(x)=\frac{1}{\frac{4}{3}}=\frac{3}{4}$

8)
$sen(x)=\frac{1}{cossec(x)}\\ \\ sen(x)=\frac{1}{\frac{3}{2}}=\frac{2}{3}\\ \\ cos(x)=\sqrt{1-sen^2(x)}\\ \\ cos(x)=\sqrt{1-(\frac{2}{3})^2}\\ \\ cos(x)=\sqrt{1-\frac{4}{9}}\\ \\ cos(x)=\sqrt{\frac{5}{6}}\\ \\ cos(x)=\frac{\sqrt5}{3}$

9)
$\frac{cotg(x).sen(x)}{cos(x)}=\\ \\ \frac{\frac{cos(x)}{sen(x)}.sen(x)}{cos(x)}=\\ \\ \frac{cos(x)}{cos(x)=1}$