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. $\frac { \sin ( x ) + \sin ( y ) } { \cos ( x ) + \cos ( y ) } + \frac { \cos ( x ) + \cos ( y ) } { \sin ( x ) + \sin ( y ) } = 1$
III. $\frac { \sin ( x ) + \cos ( y ) } { \sin ( x ) \cos ( y ) } = \sin ( y ) + \cos ( x )$
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.

Question

Quizplus · Accepted Answer

The first equation is a trigonometric identity, as it simplifies to zero using sum-to-product identities. The other equations do not hold true for all values of x and y.