Question

Calculando-se a expressão $\frac{1}{sen(105^o)-cos(75^o)}$ obtém-se

Answer 1

Vamos lá:

$\text{vamos calcular}\ sen(105)^{\circ}-cos(75)^{\circ}:\\ \\ sen105^{\circ}=\sqrt{2}(\sqrt{3}+1)\\ \\ cos75^{\circ}=\sqrt{2}(\sqrt{3}-1)\\ \\ \sqrt{2}(\sqrt{3}+1)-\sqrt{2}(\sqrt{3}-1)\\ \\ \sqrt{6}+\sqrt{2}-(\sqrt{6}-\sqrt{2})\\ \\ 2\sqrt{2}\\ \\ \text{ent\~ao:}\\ \\ \frac{1}{2\sqrt{2}}\\ \\ \frac{1}{2\sqrt{2}}\times \frac{2\sqrt{2}}{2\sqrt{2}}\\ \\ \frac{2\sqrt{2}}{4\sqrt{4}}\\ \\ \frac{1\sqrt{2}}{2\cdot 2}\\ \\ \boxed{\frac{\sqrt{2}}{4}}$

Espero ter ajudado.