f(x)=cos平方x-sin平方x+2倍根号3sinxcosx+1 求f(x)的最小正周期及单调区间?
问题描述：
f(x)=cos平方x-sin平方x+2倍根号3sinxcosx+1 求f(x)的最小正周期及单调区间?
答
f(x)=cos2x+√3sin2x+1
=2sin(2x+π/6)＋1,
T＝π,
2kπ-π/2≤2x+π/6≤2kπ+π/2,
kπ-π/3≤x≤kπ+π/6.
又2kπ＋π/2≤2x+π/6≤2kπ+3π/2,
kπ＋π/6≤x≤kπ+2π/3.
∴f(x)的最小正周期是π,
单调增区间是[kπ-π/3,kπ+π/6],k∈Z.
单调减区间是[kπ＋π/6,kπ+2π/3],k∈Z.