已知函数F(x)=根号3(sin^2X-cos^2X)+2sinXcosX.(1)X属于[0,2π/3]时，求F(x)的值域。
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F(x)=根号3(sin^2X-cos^2X)+2sinXcosX
=√3cos2x+sin2x
=2sin(2x+π/3)
(1) X属于[0,2π/3] 2x+π/3属于[π/3，5π/3]
2sin(2x+π/3)属于[-2，2]
值域为 [-2，2]
（2）
2kπ-π/2<=2x+π/3<=2kπ+π/2
kπ-5π/12<=x<=kπ+π/12
递增区间[kπ-5π/12，kπ+π/12] k∈Z
=√3cos2x+sin2x
=2sin(2x+π/3)
(1) X属于[0,2π/3] 2x+π/3属于[π/3，5π/3]
2sin(2x+π/3)属于[-2，2]
值域为 [-2，2]
（2）
2kπ-π/2<=2x+π/3<=2kπ+π/2
kπ-5π/12<=x<=kπ+π/12
递增区间[kπ-5π/12，kπ+π/12] k∈Z
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