Question

已知函数f(x)=根号3倍sinx/2cosx/2+cos^2x/2+1/2求f(x)单调减区间

Answer 1

f(x)=√3sin(x/2)cos(x/2)+cos²(x/2)+1/2
=√3/2sinx+(cosx+1)/2+1/2
=√3/2sinx+1/2cosx+1
=sin(x+π/6)+1
令2kπ+π/2≤x+π/6≤2kπ+3π/2 (k∈N)
则2kπ+π/3≤x≤颂改2kπ+4π/物乱3 (k∈N)
∴f(x)的野蚂判单调递减区间为[2kπ+π/3,2kπ+4π/3](k∈N)

Answer 2

f(x)=根号3倍sinx/2cosx/2+cos^2x/2+1/2
=√3/2*sinx+(cosx+1)/2+1/2
=sin(x+π/6)+3/2
所以f(x)单调减区间为稿脊耐[2nπ+π/2-π/6,2nπ+3π/野厅2-π/6]
既[2nπ+π/3,2nπ+4π/键春3]

Answer 3

f(x)=根号3倍sinx/2cosx/2+cos^2x/2+1/2
=(√3/2)sinx+1/2*【2*cos^2x/2-1】+1
=(√3/2)sinx+1/2cosx+1
=sin(x+Π/6)+1
就可含差以缺州知道f(x)的单调减区伏老蔽间是【Π/3+2kΠ,4Π/3+2kΠ】