Solve the Problem $\mathrm { P } ( \mathrm { t } ) = \frac { \mathrm { a } } { 8 } \cos ( 2 \mathrm { n } \pi - \mathrm { ct } )$

Multiple Choice

Solve the problem.
-In a particular situation, the pressure, P, exerted on a person's eardrum at a distance of 8 feet from the source is given by the function: $\mathrm { P } ( \mathrm { t } ) = \frac { \mathrm { a } } { 8 } \cos ( 2 \mathrm { n } \pi - \mathrm { ct } )$ , where $\mathrm { n }$ is a positive integer. Use the difference identity for cosine to simplify $\mathrm { P }$ in this situation.

A) $\mathrm { P } ( \mathrm { t } ) = \frac { \mathrm { a } } { 8 } \cos ( \mathrm { ct } )$
B) $\mathrm { P } ( \mathrm { t } ) = \frac { 8 } { 9 } \cos ( \mathrm { ct } + 8 )$
C) $\mathrm { P } ( \mathrm { t } ) = \frac { \mathrm { a } } { 8 } \cos ( \mathrm { ct } ) - \frac { \mathrm { a } } { 8 } \sin ( \mathrm { ct } )$
D) $\mathrm { P } ( \mathrm { t } ) = \cos ( \mathrm { ct } )$