|a+b|=√[cos^2(3x/2)+2cos(3x/2)cos(x/2)+cos^2(x/2)+sin^2(3x/2)-2sin(3x/2)sin(x/2)+sin^2(x/2)]

=√[2+2cos(3x/2)cos(x/2)-2 sin(3x/2)sin(x/2)]

=√[2+2co(3x/2+x/2)]

=√[2+2cos2x]

=√[2( 1+cos2x)]

=√4cos^2(x)

=2|cosx|