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f(x)=2cos²ωx+2√3sinωxcosωx+3
=(2cos²ωx-1)+√3sin2ωx+4
=cos2ωx+√3sin2ωx+4
=2[(1/2)cos2ωx+(√3/2)sin2ωx]+4
=2sin[2ωx+(π/6)]+4
最小正周期T=2π/(2ω)=π
所以,ω=1
当ω=1时,f(x)=2sin[2x+(π/6)]+4
单调递增区间为:2x+(π/6)∈[2kπ-(π/2),2kπ+(π/2)](k∈Z)
==> 2x∈[2kπ-(2π/3),2kπ+(π/3)](k∈Z)
==> x∈[kπ-(π/3),kπ+(π/6)](k∈Z)
单调递减区间为:2x+(π/6)∈[2kπ+(π/2),2kπ+(3π/2)](k∈Z)
==> 2x∈[2kπ+(π/3),2kπ+(4π/3)](k∈Z)
==> x∈[kπ+(π/6),kπ+(2π/3)](k∈Z)
=(2cos²ωx-1)+√3sin2ωx+4
=cos2ωx+√3sin2ωx+4
=2[(1/2)cos2ωx+(√3/2)sin2ωx]+4
=2sin[2ωx+(π/6)]+4
最小正周期T=2π/(2ω)=π
所以,ω=1
当ω=1时,f(x)=2sin[2x+(π/6)]+4
单调递增区间为:2x+(π/6)∈[2kπ-(π/2),2kπ+(π/2)](k∈Z)
==> 2x∈[2kπ-(2π/3),2kπ+(π/3)](k∈Z)
==> x∈[kπ-(π/3),kπ+(π/6)](k∈Z)
单调递减区间为:2x+(π/6)∈[2kπ+(π/2),2kπ+(3π/2)](k∈Z)
==> 2x∈[2kπ+(π/3),2kπ+(4π/3)](k∈Z)
==> x∈[kπ+(π/6),kπ+(2π/3)](k∈Z)
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