y'=cosx*cos^2(x/2)-sinx*2cos(x/2)*sin(x/2)1/2=cosxcos^2(x/2)-sin^2x/2
y'=0
1/2cosx*(1+cosx)-(1-cos^2x)=0
1/2cosx+1/2cos^2x-1+cos^2x=0
3/2cos^2x+1/2cosx-1=0
cosx=t
3t^2+t-2=0
t1=-1 x=П
t2=2/3 х=arccos2/3
y(П)=0 - минимум
cosx=2/3 cos^2x/2=1/2(1+2/3)=5/6
sinx=sqrt(1-4/9)=sqrt(5)/3
y=(5/18)*sqrt(5)- максимум