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

I is the only identity because it can be simplified to $0 = 0$, which is always true. II and III are not identities because they cannot be simplified to $0 = 0$.