Verify That the Equation Is an Identity $\mathrm { P }$

Verify that the equation is an identity.
-In a particular situation, the pressure, $\mathrm { P }$ , exerted on a person's eardrum at a distance of 6 feet fron the source is given by the function: $\mathrm { P } ( \mathrm { t } ) = \frac { \mathrm { a } } { 6 } \cos ( 2 \mathrm { n } \pi - \mathrm { ct } )$ , where $\mathrm { n }$ is a positive integer. Use the difference identity for cosine to simplify $\mathrm { P }$ in this situation.

A) $P ( t ) = \frac { a } { 6 } \cos ( c t ) - \frac { a } { 6 } \sin ( c t )$
B) $P ( t ) = \frac { a } { 6 } \cos ( c t )$
C) $\mathrm { P } ( \mathrm { t } ) = \cos ( \mathrm { ct } )$
D) $\mathrm { P } ( \mathrm { t } ) = \frac { 6 } { 7 } \cos ( \mathrm { ct } + 6 )$