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Determine Which of the Following Are Trigonometric Identities sin⁡(t)+sin⁡(s)cos⁡(t)−cos⁡(s)+cos⁡(t)+cos⁡(s)sin⁡(t)−sin⁡(s)=0\frac { \sin ( t ) + \sin ( s ) } { \cos ( t ) - \cos ( s ) } + \frac { \cos ( t ) + \cos ( s ) } { \sin ( t ) - \sin ( s ) } = 0

Question 51

Multiple Choice

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

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