Question

a questão 17, letra A e B.

Answer 1

a)
$\frac{a^2.cos180^o+b^2.cos0^o}{-a.cos45^o+b.cos225^o}=\frac{a^2.(-1)+b^2.1}{-a.\frac{\sqrt2}{2}+b.(-\frac{\sqrt2}{2})}=\frac{b^2-a^2}{\frac{\sqrt2}{2}.(b-a)}=\frac{(b+a)(b-a)}{\frac{\sqrt2}{2}(b-a)}=\frac{b+a}{\frac{\sqrt2}{2}}=\\ \\ \\ =\frac{2(a+b)}{\sqrt2}=\sqrt2(a+b)$

b)
$\frac{(a+b).cos\frac{3\pi}{4}+b.cos\frac{3\pi}{2}}{a.cos\frac{\pi}{4}+b.cos\frac{7\pi}{4}}=\frac{(a+b).(-\frac{\sqrt2}{2})+b.0}{a.\frac{\sqrt2}{2}+b.\frac{\sqrt2}{2}}=\frac{(-\frac{\sqrt2}{2})(a+b)}{\frac{\sqrt2}{2}(a+b)}=-1$