Solve the Equation for Solutions Over the Interval [0, 2π) $$\sin \frac { x } { 2 } + \cos \frac { x } { 2 } = \sqrt { 2 }$$

Solve the equation for solutions over the interval [0, 2π) . Write solutions as exact values or to four decimal places, as
appropriate.
- $$\sin \frac { x } { 2 } + \cos \frac { x } { 2 } = \sqrt { 2 }$$

A) $\left\{ \frac { \pi } { 4 } \right\}$
B) $\{ \pi \}$
C) $\{ 0 , \pi \}$
D) $\left\{ \frac { \pi } { 2 } \right\}$