Determine which of the following are trigonometric identities.
I. $\frac { \cos ( \mathrm { t } ) - \cos ( \mathrm { s } ) } { \sin ( \mathrm { t } ) + \sin ( \mathrm { s } ) } + \frac { \sin ( \mathrm { t } ) - \sin ( \mathrm { s } ) } { \cos ( \mathrm { t } ) + \cos ( \mathrm { s } ) } = 0$
II. $\frac { \cos ( \mathrm { t } ) + \cos ( \mathrm { s } ) } { \sin ( \mathrm { t } ) + \sin ( \mathrm { s } ) } + \frac { \sin ( \mathrm { t } ) + \sin ( \mathrm { s } ) } { \cos ( \mathrm { t } ) + \cos ( \mathrm { s } ) } = 1$
III. $\frac { \cos ( \mathrm { t } ) + \sin ( \mathrm { s } ) } { \cos ( \mathrm { t } ) \sin ( \mathrm { s } ) } = \cos ( \mathrm { s } ) + \sin ( \mathrm { t } )$
A) I is the only identity.
B) I, II, and III are identities.
C) II is the only identity.
D) II and II are the only identities.
E) I and II are the only identities.

Question

Quizplus · Accepted Answer

I is a trigonometric identity derived from the sum-to-product formulas. II and III do not hold as general identities for all values of $t$ and $s$.

Determine Which of the Following Are Trigonometric Identities II III