Question

I attempted to use cos(u) - cos (v)= 2*sin((u+v/)2)*sin((u-v)/2)
2*sin(((x+pi/3)+(x-pi/3)/)2)*sin((x+pi/3)-(x-pi/3)/2)
2* sin(x) * sin( pi/3)
2* sqrt(3)/2* sin(x)
sqrt(3)*sin(x) = -sqrt(3)
sin(x)= -sqrt(3)/ sqrt(3)
x= arcsin(-1)
That would make x = -pi/2 correct?? Why is it not an option??