已知π/2<β<α<3π/4,且cos( α-β)=12/13, sin(α+β)=-3/5,

π/2<β<α<3π/4,第二象限
π<α+β<3π/2第三象限
0<α-β<π/4第一象限

cos( α-β)=12/13==> sin( α-β)=5/13,
sin(α+β)=-3/5==>cos(α+β)=-4/5

sin2α
=sin(α+β + α-β)
=sin(α+β)cos(α-β)+cos(α+β)sin(α-β)
=-3/5*12/13 -4/5*5/13
=-56/65

cos2β
=cos(α+β - α-β)
=cos(α+β)cos(α-β)+sin(α+β)sin(α-β)
=-4/5*12/13 -3/5*5/13
=-63/65

=

抱歉，我的手机打不出希腊字母！sin=(-56/65) cos=(-63/65)