Question

！在线等！已知函数f(x)=2根号3sinxcosx+2cos^2x-1(x属于R），（1）求函数f(x)的单调递减区间，（2）若A是

Answer 1

f(x)=2√3sinxcosx+2（cosx）^2-1
=√3sin2x+cos2x
=2(sin2xcosπ/6+cos2xsinπ/6)
=2sin(2x+π/6），
2kπ+π/2≤2x+π/6≤2kπ+3π/2，单调递减，k∈Z，
函数f(x)的单调递减区间：kπ+π/6≤x≤kπ+2π/3，k∈Z
∴x∈[kπ+π/6，kπ+2π/3]，k∈Z。