已知sin(α+π/4)=-5/13,则:
sin2α=-cos(π/2 + 2α)
=-[1- 2sin²(α+π/4)]
=-[1- 2*(25/169)]
=-119/169为什么sin2α=-cos(π/2 + 2α)？因为cos(π/2 + 2α)=cos[π/2 -(- 2α)]=sin(-2α)=-sin2α为什么-cos(π/2 + 2α)=-[1- 2sin²(α+π/4)]因为：cos(π/2 + 2α)=cos[2(α + π/4)]=1- 2sin²(α+π/4)(倍角公式)