f(x)=2根号下3sin(π-x)sin(π/2-x)-2cos(π+x)cosx+2
=2cosx(根号下3sinx+cosx)+2
=根号下3sin2x+cos2x+3
=2sin(2x+π/6)+3
最小正周期=2π÷2=π
单调递减区间：
2kπ+π/2<=2x+π/6<=2kπ+3π/2
kπ+π/6<=x<=kπ+2π/3
(2) f(A)=2sin(2A+π/6)+3=4
sin(2A+π/6)=1/2
2A+π/6=5π/6
A=π/3
△ABC面积=bcsinA÷2=根号下3/2
c=2
a²=b²+c²-2bccosa
=1+4-2
=3
a=根号下3
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