Due to:

Vector a

=(sin(π/2+x)，√3cosx)

=(cosx，√3cosx)

f(x)

=a*b

=(cosx，√3cosx)*(sinx，cosx)

=sinxcosx+√3cos^2(x)

=( 1/2)(2 sinxcosx)+√3 *( 1+cos2x)/2

=( 1/2)sin2x+(√3/2)cos2x+√3/2

=sin(2x+π/3)+(√3/2)