求函数y=2cos(x+π/4)*cos(x-π/4)+(√3)sin2x

y=2cos(x+π/4)*cos(x-π/4)+(√3)sin2x
=2sin(π/4-x)*cos(π/4-x)+(√3)sin2x
=sin(π/2-2x)+(√3)sin2x
=cos2x+(√3)sin2x
=2[cosπ/3cos2x+sinπ/3sin2x]
=2cos(2x-π/3)
所以,值域[-2,2],周期为π,
2kπ<2x-π/3<(2k+1)π,kπ+π/6<x<kπ+2π/3为单调减区间,其余为单调增区间
对称轴2x-π/3=kπ,x=kπ/2+π/6
对称中心2x-π/3=kπ+π/2,x=kπ/2+5π/12,y=0
奇偶性,非奇函数,非偶函数

y=2sin(2x-π/6)
值域 [-2,2]
周期 π
单调区间 递增为 -π/6+kπ <=x<= π/3+kπ
对称轴 x=π/3+kπ/2
对称中心 (π/12+2/π,0)
非奇非偶函数