a+b
=(cos3x/2+cosx/2,sin3x/2-sinx/2)
|a+b|^2
=(cos3x/2+cosx/2)^2+(sin3x/2-sinx/2)^2
=2+2(cos3x/2cosx/2-sin3x/2sinx/2)
=2+2cosx
0<=|a+b|^2 <= 4
0<=|a+b| <= 2