Question

calcule o valor dessa expressão

$sen ^{2} 60 + cos ^{2} 45 \: sobre \: tg ^{2} 30$

Answer 1

$\dfrac{\sin^2(60^\circ)+\cos^2(45^\circ)}{\tan^2(30^\circ)}=\\\\\\\dfrac{(\frac{\sqrt3}{2})^2+(\frac{\sqrt2}{2})^2}{(\frac{\sqrt3}{3})^2}=\\\\\\\dfrac{\frac34+\frac24}{\frac39 }=\\\\\\\dfrac{\frac54}{\frac39}=\dfrac54\cdot\dfrac93=\dfrac{15}{4}$