已知函数f(x)=cos2x减根号3sinxcosx+1

题目

已知函数f(x)=cos2x减根号3sinxcosx+1
(1)求函数f(x)的单调增区间 （2）若f（θ）=5/6 θ属于（π/3,2π/3）,求sin2θ的值

答案

f(x)=cos2x - 根号3sinxcosx +1
=cos2x - 2分之根号3sin2x +1
=cos(2x+π/3)+1
令2kπ-π≤2x+π/3≤2kπ
∴kπ-2π/3≤x≤kπ-π/6
∴f(x)的增区间是[kπ-2π/3,kπ-π/6]