f(x)=a.b
=(cosx,4sinx-2).(8sinx,2sinx+1)
=8sinxcosx+(4sinx-2)(2sinx+1)
=8sinxcosx+8(sinx)^2-2
=4sin2x +4(1-cos2x)-2
=4√2sin(2x-π/4) +2
max f(x) =4√2 +2