∵f(x)=2sin(π-x)cosx=2sinxcosx=sin2x
(1)∴T=2π/2=π
(2)∵x∈[-π/6,π/2]
∴根据图像可知f(x)max=f(π/4)=1,f(x)min=f(-π/6)=-(√3)/2