已知函数f(x)=2根号3sinxcosx+2cos方x-1(x属于R) 求函数f(x)的单调递减区间

问题描述:

已知函数f(x)=2根号3sinxcosx+2cos方x-1(x属于R) 求函数f(x)的单调递减区间

f(x)=2√3sinxcosx+2cos²x-1=√3sin2x+cos2x=2sin(2x+π/6),则递减区间是:2kπ+π/2≤2x+π/6≤2kπ+3π/2,得:kπ+π/6≤x≤kπ+2π/3,则减区间是:[kπ+π/6,kπ+2π/3],其中k∈Z