解f(x)=sin^2x+2sinxcosx+3cos^2x,
=sin^2x+cos^2x+2sinxcosx+2cos^2x
=1+sin2x+2cos^2x
=2+sin2x+2cos^2x-1
=sin2x+cos2x+2
=√2sin(2x+π/4)+2
把函数f(x)=√2sin(2x+π/4)+2
向右平移π/8个单位,向下平移2个单位得到
函数y=√2sin2x是奇函数.
把函数f(x)=√2sin(2x+π/4)+2
向左平移π/8个单位,向下平移2个单位得到
函数y=√2cos2x是偶函数.