Determine Which of the Following Are Trigonometric Identities $\cos ^ { 4 } ( \mathrm { t } ) + \sin ^ { 4 } ( \mathrm { t } ) = 1 - 2 \sin ^ { 2 } ( \mathrm { t } ) + 2 \sin ^ { 4 } ( \mathrm { t } )$

Multiple Choice

Determine which of the following are trigonometric identities.
I. $\cos ^ { 4 } ( \mathrm { t } ) + \sin ^ { 4 } ( \mathrm { t } ) = 1 - 2 \sin ^ { 2 } ( \mathrm { t } ) + 2 \sin ^ { 4 } ( \mathrm { t } )$
II. $\sin ^ { 5 } ( \mathrm { t } ) = \sin ^ { 3 } ( \mathrm { t } ) \cos ^ { 2 } ( \mathrm { t } ) - \sin ^ { 3 } ( \mathrm { t } )$
III. $\sin ^ { 3 } ( \mathrm { t } ) \cos ^ { 2 } ( \mathrm { t } ) = \left( \cos ^ { 2 } ( \mathrm { t } ) - \cos ^ { 4 } ( \mathrm { t } ) \right) \sin ( \mathrm { t } )$

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