Determine Which of the Following Are Trigonometric Identities $\frac { \sin ( y ) - \sin ( x ) } { \cos ( y ) + \cos ( x ) } + \frac { \cos ( y ) - \cos ( x ) } { \sin ( y ) + \sin ( x ) } = 0$

Determine which of the following are trigonometric identities.
I. $\frac { \sin ( y ) - \sin ( x ) } { \cos ( y ) + \cos ( x ) } + \frac { \cos ( y ) - \cos ( x ) } { \sin ( y ) + \sin ( x ) } = 0$
II. $\frac { \sin ( y ) + \sin ( x ) } { \cos ( y ) + \cos ( x ) } + \frac { \cos ( y ) + \cos ( x ) } { \sin ( y ) + \sin ( x ) } = 1$
III. $\frac { \sin ( y ) + \cos ( x ) } { \sin ( y ) \cos ( x ) } = \sin ( x ) + \cos ( y )$

A) I is the only identity.
B) II and II are the only identities.
C) I, II, and III are identities.
D) I and III are the only identities.