Solve the Multi-Angle Equation Below $\cos \left( \frac { x } { 2 } \right) = \frac { \sqrt { 2 } } { 2 }$

Multiple Choice

Solve the multi-angle equation below.
$\cos \left( \frac { x } { 2 } \right) = \frac { \sqrt { 2 } } { 2 }$

A) $\frac { \pi } { 3 } + n \pi , \frac { 7 \pi } { 3 } + n \pi$ , where $n$ is an integer
B) $\frac { \pi } { 3 } + 2 n \pi , \frac { 7 \pi } { 3 } + 2 n \pi$ , where $n$ is an integer
C) $\frac { \pi } { 2 } + n \pi , \frac { 7 \pi } { 3 } + n \pi$ , where $n$ is an integer
D) $\frac { \pi } { 2 } + n \pi , \frac { 7 \pi } { 2 } + n \pi$ , where $n$ is an integer
E) $\frac { \pi } { 2 } + 4 n \pi , \frac { 7 \pi } { 2 } + 4 n \pi$ , where $n$ is an integer