No. 20_Soal Asli UTBK 2019 Matematika Saintek

---

Diketahui system persamaan:
$\left\{ \begin{array}{*{35}{l}}   \cos 2x+\cos 2y=-\frac{1}{8},\,dengan\,0 < x,y <\frac{1}{2}\pi   \\   \cos x=2\cos y  \\ \end{array} \right.$
Nilai dari ${{\sin }^{2}}x$ = …
A. $\frac{3}{8}$
B. $\frac{3}{4}$
C. $\frac{2}{4}$
D. $\frac{1}{4}$
E. $\frac{1}{8}$