a.b
=(cos3x/2,sin3x/2).(cosx/2,-sinx/2)
=cos2x
a+b = (cos3x/2+cosx/2,sin3x/2-sinx/2)
|a+b|^2
= (cos3x/2+cosx/2)^2+(sin3x/2-sinx/2)^2
= 2+2cos2x
= (2cosx)^2
|a+b|= 2cosx
a.b
=(cos3x/2,sin3x/2).(cosx/2,-sinx/2)
=cos2x
a+b = (cos3x/2+cosx/2,sin3x/2-sinx/2)
|a+b|^2
= (cos3x/2+cosx/2)^2+(sin3x/2-sinx/2)^2
= 2+2cos2x
= (2cosx)^2
|a+b|= 2cosx