Find All Solutions of the Given Equation in the Interval $$\frac { 1 } { 2 } \sin 2 x = \cos x$$

Multiple Choice

Find all solutions of the given equation in the interval [0,2π) . ​​ $$\frac { 1 } { 2 } \sin 2 x = \cos x$$ ​

A) ​ $x = \frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$
B) ​ $x = 0 , \frac { \pi } { 2 } , \pi$
C) ​ $x = 0 , \pi , \frac { \pi } { 2 } , \frac { 3 \pi } { 4 }$
D) ​ $x = 0 , \pi$
E) ​x = 0