f(x)=1/2(cos2x+1)+1/2sin2x
=1/2(cos2x+sin2x)+1/2
=根2/2(根2/2sin2x+根2/2cos2x)+1/2
=根2/2sin(2x+π/4)+1/2
所以,最小正周期为π
最小值为1/2-根2/2,此时x=5π/8
最大值为1/2+根2/2,此时x=π/8
f(x)=1/2(cos2x+1)+1/2sin2x
=1/2(cos2x+sin2x)+1/2
=根2/2(根2/2sin2x+根2/2cos2x)+1/2
=根2/2sin(2x+π/4)+1/2
所以,最小正周期为π
最小值为1/2-根2/2,此时x=5π/8
最大值为1/2+根2/2,此时x=π/8