化简f(x)=cos((6k+1)/3*π+2x)+cos((6k-1)/3*π-2x)(x∈R,k∈Z),并求函数f(x)的值域和最小正周期

cos[(6k+1)π/3+2x]=cos[2kπ+π/3+2x]=cos[π/3+2x] cos[(6k-1)π/3-2x]=cos[2kπ-π/3-2x]=cos[π/3+2x] 那么原式=2cos[π/3+2x]+2√3sin(π/6-2x) 2√3sin(π/6-2x)=2√3sin[π/2-(π/3+2x)]=2√3cos(π/3+2x) 即...