已知f(x)=2sinxcosx-2根号3(cosα)^2+根号3,若f(α)=10/13,且α属于【π/2,π】,求sin2α的值
问题描述：
已知f(x)=2sinxcosx-2根号3(cosα)^2+根号3,若f(α)=10/13,且α属于【π/2,π】,求sin2α的值
答
f(x)=2sinxcosx-2√3(cosα)^2+√3=sin2x-√3(2(cosα)^2-1)=sin2x-√3cos2x=2sin(2x-π/3)f(α)=10/13∴2sin(2α-π/3)=10/13sin(2α-π/3)=5/13,∵α属于[π/2,π],2α-π/3为第二象限角∴cos(2α-π/3)=-12/13sin...