Suppose $x, y \in (0, \pi/2)$ and $x \neq y$. Which of the following statement is true?\\
(A) $2\sin(x + y) < \sin 2x + \sin 2y$ for all $x, y$.\\
(B) $2\sin(x + y) > \sin 2x + \sin 2y$ for all $x, y$.\\
(C) There exist $x, y$ such that $2\sin(x + y) = \sin 2x + \sin 2y$.\\
(D) None of the above.