Question

已知函数f(x)=1+2根号3sinxcosx+2cos^2x,

Answer 1

f(x)=2＋√3sin2x＋cos2x=2sin(2x＋π/6)＋2

1、增区间：2kπ－π/2≤2x＋π/6≤2kπ＋π/2

kπ－π/3≤x≤kπ＋π/6

则：增区间是：[kπ－π/3,kπ＋π/6],其中k是整数

2、f(a)=2sin(2a＋π/6)＋2=3,得：sin(2a＋π/6)=1/2,2a＋π/6=5π/6,得：a=π/3