F(X)=2√3sinx*cosx+2cos^2x-11,求函数F(X)的最小正周期及在区间【0,π/2】上得最值2,若F(X)=6/5,X∈ 【π/4,π/2】,求COS2X3,求Y=F(X)得单调增区间

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F(X)=2√3sinx*cosx+2cos^2x-11,求函数F(X)的最小正周期及在区间【0,π/2】上得最值2,若F(X)=6/5,X∈【π/4,π/2】,求COS2X3,求Y=F(X)得单调增

F(X)=2√3sinx*cosx+2cos^2x-11,求函数F(X)的最小正周期及在区间【0,π/2】上得最值2,若F(X)=6/5,X∈ 【π/4,π/2】,求COS2X3,求Y=F(X)得单调增区间
F(X)=2√3sinx*cosx+2cos^2x-1
1,求函数F(X)的最小正周期及在区间【0,π/2】上得最值
2,若F(X)=6/5,X∈ 【π/4,π/2】,求COS2X
3,求Y=F(X)得单调增区间

F(X)=2√3sinx*cosx+2cos^2x-11,求函数F(X)的最小正周期及在区间【0,π/2】上得最值2,若F(X)=6/5,X∈ 【π/4,π/2】,求COS2X3,求Y=F(X)得单调增区间
F(X)=2√3sinx*cosx+2cos^2x-1
=√3sin2x+cos2x
=2sin﹙2x+π/6﹚
⑴求函数F(X)的最小正周期π,
∵0≤x≤π/2,∴π/6≤2x+π/6≤7π/6,∴-1/2≤F(X)≤1/2
∴F(X)max=1/2,F(X)min=-1/2
⑵2sin﹙2x+π/6﹚=6/5,.∴sin﹙2x+π/6﹚=3/5
∴COS2X=﹙3+4√3﹚/10
⑶2kπ-π/2≤2x+π/6≤2kπ+π/2
∴kπ-π/3≤x≤kπ+π/6,k∈z
单调增区间﹛XIkπ-π/3≤x≤kπ+π/6,k∈z﹜