f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)
=cos2xcosπ/3+sin2xsinπ/3+2sin(x-π/4)sin（x+π/4-π/2+π/2）
=1/2cos2x+√3/2sin2x+2sin(x-π/4)cos(x-π/4)
=1/2cos2x+√3/2sin2x+sin2(x-π/4)
=1/2cos2x+√3/2sin2x+sin(2x-π/2)
=1/2cos2x+√3/2sin2x-cos2x
=√3/2-1/2cos2x
=sin(2x-π/6)
(1)
最小正周期：T=2π/2=π
對(duì)稱(chēng)軸：
2x-π/6=π/2+kπ（k∈Z）
2x=2π/3+kπ
x=π/3+kπ/2
（2）
2x-π/6=-π/2+2kπ（k∈Z）
2x=-π/3+2kπ
x=-π/6+kπ
2x-π/6=π/2+2kπ（k∈Z）
2x=2π/3+2kπ
x=π/3+kπ
當(dāng)x=-π/12時(shí),f（x）=-√3/2
當(dāng)x=π/3是,f（x）=1
f（x）在區(qū)間[-π /12,π /2]上的值域 為[-√3/2,1]