The set of solutions of the system of equations
$
\begin{aligned}
x+y & =\frac{2 \pi}{3} \\
\text{and} \quad \cos x+\cos y & =\frac{3}{2},
\end{aligned}
$
where $x, y$ are real,is

• A
  $\{(x, y): \cos \left(\frac{x-y}{2}\right)=\frac{1}{2}\}$
• B
  $\{(x, y): \sin \left(\frac{x-y}{2}\right)=\frac{1}{2}\}$
• C
  $\{(x, y): \cos (x-y)=\frac{1}{2}\}$
• D
  Empty set