sec(x/2) = 1/cos(x/2)
sec(x/2)=cos(x/2) ----> cos^2(x/2)=1 ---> cos(x/2) = -1 and cos(x/2) = 1
Cos(x/2)=1 --- > x/2 = 0, only. x = 0;
cos(x/2)=-1 ----> x/2 = pi -> x = 2pi. But the statement says [0,2pi), so 2pi can not be chosen.
Only x = 0.
In fact, your equation is equivalent to sec(x)=cos(x), for x in [ 0, pi), so yes, only x = 0 .
