Question

Resolvam essa expressão com seno, consseno e tangente:

tg²30° + sen°60
____________
cos 45° . sen 45°

Obg

Answer 1

$\dfrac{\mathrm{tg^2\,}30^{\circ}+\mathrm{sen^2\,}60^{\circ}}{\cos 45^{\circ}\cdot \mathrm{sen\,}45^{\circ}}\\\\\\ =\dfrac{\left(\frac{\sqrt{3}}{3} \right )^{\!\!2}+\left(\frac{\sqrt{3}}{2} \right )^{\!\!2}}{\frac{\sqrt{2}}{2}\cdot \frac{\sqrt{2}}{2}}\\\\\\ =\dfrac{\frac{3}{9}+\frac{3}{4}}{\frac{2}{4}}\\\\\\ =\dfrac{\frac{12}{36}+\frac{27}{36}}{\frac{2}{4}}\\\\\\ =\dfrac{\left(\frac{12+27}{36} \right )}{\frac{2}{4}}\\\\\\ =\dfrac{39}{36}\cdot \dfrac{4}{2}\\\\\\ =\dfrac{13}{12}\cdot 2\\\\\\ =\dfrac{13}{6\cdot \diagup\!\!\!\! 2}\cdot \diagup\!\!\!\! 2\\\\\\ =\dfrac{13}{6}$


Bons estudos! :-)