f(x)=2sinxcosx+2sin(x+π/4)sin(x+3π/4)+1=sin2x+2sin(x+π/4)sin(sin[π/2+( x+π/4)]+1=sin2x+2sin(x+π/4)cos( x+π/4)+1=sin2x+sin(2x+π/2)+1=sin2x+cos2x+1=√2sin(2x+π/4) +1