y=sin(x/2)+cos(x/2)=2[1/2*sin(x/2)+√3/2cos(x/2)]=2*[cos60*sin(x/2)+sin60*cos(x/2)]=2*sin(x/2+60)
所以y最大值为2,当为2时,sin(x/2+60)=1,所以x/2+60=2kπ+π/2
即x/2+π/3=2kπ+π/2,x=kπ+π/3
y=sin(x/2)+cos(x/2)=2[1/2*sin(x/2)+√3/2cos(x/2)]=2*[cos60*sin(x/2)+sin60*cos(x/2)]=2*sin(x/2+60)
所以y最大值为2,当为2时,sin(x/2+60)=1,所以x/2+60=2kπ+π/2
即x/2+π/3=2kπ+π/2,x=kπ+π/3