Suppose $x , y \in ( 0 , \pi / 2 )$ and $x \neq y$. Which of the following statements is true?\\
(a) $2 \sin ( x + y ) < \sin 2 x + \sin 2 y$ for all $x , y$.\\
(b) $2 \sin ( x + y ) > \sin 2 x + \sin 2 y$ for all $x , y$.\\
(c) There exist $x , y$ such that $2 \sin ( x + y ) = \sin 2 x + \sin 2 y$.\\
(d) None of the above.