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

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

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

Correct Answer:

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