有网友碰到这样的问题“已知函数f（X)=sin²x+2根号3sinxcosx-cos²x”。小编为您整理了以下解决方案，希望对您有帮助：
解决方案1：
f(x)=sin²x+2√3sinxcosx-cos²x
=2√3sinxcosx-(cos²x-sin²x)
=√3sin(2x)-cos(2x)
=2sin(2x-π/6)
1)2kπ-π/2≤2x-π/6<2kπ+π/2
kπ-π/6≤x<kπ+π/3
2kπ+π/2≤2x-π/6<2kπ+3π/2
kπ+π/3≤x<kπ+5π/6
单增区间：[kπ-π/6,kπ+π/3]
单减区间：[kπ+π/3,kπ+5π/6]
2)f(x)最大值为2
sin(2x-π/6)=1
2x-π/6=2kπ+π/2
x=kπ+π/3