Find All Solutions in the Interval [0, 2π) $$\sin \left( \frac { x } { 2 } \right) = 2 \cos ^ { 2 } x - 1$$

Multiple Choice

Find all solutions in the interval [0, 2π) .
- $$\sin \left( \frac { x } { 2 } \right) = 2 \cos ^ { 2 } x - 1$$

A) $\frac { \pi } { 5 } , \pi , \frac { 9 \pi } { 5 }$
B) $\frac { \pi } { 3 } , \pi , \frac { 5 \pi } { 3 }$
C) $\frac { \pi } { 5 } , \frac { 9 \pi } { 5 }$
D) $0 , \pi$