Question

已知函数f（x）=根号3sinxcosx-sin∧x+1/2,x∈R 求最小正周期和最大值及取得最大值时自变量x的集合

Answer 1

f（x）=√3sinxcosx-sin^2x+1/2

=√3/2*sin2x-1/2(1-cos2x)+1/2

=√3/2sin2x+1/2cos2x

=sin(2x+π/6)

f(x)最小正周期T=2π/2=π

当2x+π/6=2kπ+π/2,k∈Z

即x=kπ+π/6,k∈Z时,

f(x)取得最大值1

f(x)取得最大值时,x的集合为

{x|x=kπ+π/6,k∈Z}