(1/2)高三数学函数。f(x)=cos(2x-派/3)+2sin(x-派/4)sin(x+派/4)。求函数最小正周期和最大值时x集合？...

f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4) =cos(2x-π/3)+cos(-π/2)-cos2x【积化和差】 =cos(2x-π/3)-cos2x =2sin(π/6)sin(2x-π/6)【和差化积】 =sin(2x-π/6) 最小正周期=2π/2 2x-π/6∈2kπ+π/2