Question

已知函数f（x）＝sin2x-2根号3sin^2x+根号3+1，求f(x)的最小正周期及其单调区间。

已知函数f（x）＝sin2x-2根号3sin^2x+根号3+1，求f(x)的最小正周期及其单调区间。急求答案！谢谢！很急

Answer 1

f(x)=sin2x-2√3sin^2x+√3+1

=sin2x+√3(-2sin^2x+1)+1

=(sin2x+√3cos2x)+1

=(sin2xcos(π/3)+cos2xsin(π/3))*2+1

=2sin(2x+π/3)+1

最小正周期=π

-π/2+2kπ<2x+π/3<π/2+2kπ  单增

-5π/12+kπ<x<π/12+kπ

π/2+2kπ<2x+π/3<3π/2+2kπ  单减

π/12+kπ<x<7π/12+kπ