Question

(trigonometria) resolva a expressão: E= sen²45º+cos⁴60º

Answer 1

Sabemos que

$\mathrm{sen\,}45^{\circ}=\dfrac{\sqrt{2}}{2}\;\;\;\text{ e }\;\;\;\cos 60^{\circ}=\dfrac{1}{2}.$

Portanto,

$E=\mathrm{sen^{2}\,}45^{\circ}+\cos^{4}60^{\circ}\\ \\ E=\left(\dfrac{\sqrt{2}}{2} \right )^{2}+\left(\dfrac{1}{2} \right )^{4}\\ \\ \\ E=\dfrac{2}{4}+\dfrac{1}{16}\\ \\ \\ E=\dfrac{8+1}{16}\\ \\ \\ \boxed{\begin{array}{c}E=\dfrac{9}{16} \end{array}}$