3cos^2x+2cosxsinx+sin^2x
=cos^2x+sin^2x+2cosxsinx +2cos^2x
=1+sin2x+2cos^2x
=1+sin2x+1+cos2x
=2+sin2x+cos2x
=2+√2(√2/2sin2x+√2/2cos2x)
=sin(2x+π/4)+2