已知函数f(x)=2sinxcosx+2cosx的平方-1.求函数f(x)的最小正周期

f(x)=2sinxcosx+2cosx的平方-1 =sin(2x)+cos(2x) =根号2[根号2/2·sin(2x)+根号2/2·cos(2x)] =根号2[cos(π/4)·sin(2x)+根号2/2·cos(2x)] =根号2sin(2x+π/4) =根号2sin(2π+2x+π/4) =根号2sin[2(π+x)+π/4]； ...