答：cos(x+π/4)=-sin(x+π/4-π/2)=-sin(x-π/4)所以f(x)=cos²(x-π/4)-cos²(x+π/4)=cos²(x-π/4)-sin²(x-π/4)=cos(2x-π/2)=-sin2xT=2π/|w|=2π/2=π周期是π.