使用降幂公式(sinx)^2=(1-cos2x)/2
原式可化为y=(1-cos(2x+π/2))/2-(1-cos(2x-π/2))/2
=-cos(2x+π/2)/2+cos(2x-π/2)/2
=sin2x/2+sin2x/2
=sin2x
∴原函数是周期为π的奇函数.