求2根3cosx^2+sin2x的最小正周期和单调减区间

y=2√3cos²x+sin2x
=2√3(1+cos2x)/2+sin2x
=sin2x+√3cos2x+√3
=√[1²+(√3)²]sin(2x+z)+√3
=2sin(2x+z)+√3
其中tanz=√3/1=√3
z=π/3
y=2sin(2x+π/3)+√3

所以T=2π/2=π

y单调减则sin单调减
sinx的减区间是(2kπ+π/2,2kπ+3π/2)
所以2kπ+π/2<2x+π/3<2kπ+3π/2
2kπ+π/6<2x<2kπ+7π/6
kπ+π/12<x<kπ+7π/12
所以单调减区间是(kπ+π/12，kπ+7π/12),k是整数