设函数,f（x）=2cos^2x+√3sin2x,若f（x）=5/3,-π/6＜x＜π/6,求sin2x

题目

设函数,f（x）=2cos^2x+√3sin2x,若f（x）=5/3,-π/6＜x＜π/6,求sin2x

答案

f（x）=2cos^2x+√3sin2x=cos2x+1+√3sin2x
=2sin(2x+π/6)+1=5/3
=> sin(2x+π/6)=1/3
-π/2