[sin(x/2)+cos(x/2)]²
=sin²(x/2)+2sin(x/2)cos(x/2)+cos²(x/2)
=1+sinx
=4/3
2ππ第三象限
所以
sin(x/2)<0,cos(x/2)<0
sin(x/2)+cos(x/2)<0
所以sin(x/2)+cos(x/2)=-2√3/3