将函数f(x)=sin^2x+sin2x+3cos^2x写成f(x)=Asin(wx+n)+k的形式

f(x)=sin^2x+sin2x+3cos^2x
=sin^2x+2sinxcosx+3cos^2x
=sin^2x+2sinxcosx+cos^2x+2cos^2x
=1+sin2x+2cos^2x-1+1
=sin2x+cos2x+2
=√2(√2/2sin2x+√2/2cos2x)+2
=√2(sin2xcosπ/4+cos2xsinπ/4)+2
=√2sin(2x+π/4)+2