Question

Calcule o valor das expressões abaixo:​

Answer 1

Sabendo que π rad = 180º temos:

$\dfrac{\sin30^{\circ}+\sin60^{\circ}}{\sin180^{\circ}-\sin45^{\circ}} =\dfrac{\frac{1}{2} +\frac{\sqrt{3} }{2}}{0-\frac{\sqrt{2} }{2}} =\dfrac{\frac{1+\sqrt{3} }{2}}{-\frac{\sqrt{2} }{2}} =\dfrac{1+\sqrt{3} }{2}\cdot\bigg(-\dfrac{2}{\sqrt{2} }\bigg)=\\\\\\=-\dfrac{1+\sqrt{3} }{\sqrt{2} }=-\dfrac{1+\sqrt{3} }{\sqrt{2} }\cdot\dfrac{\sqrt{2} }{\sqrt{2} }=-\dfrac{\sqrt{2} +\sqrt{6} }{2}$