设0<α<β<π/2,且cos(α+β)=-5/13,cos(α-β)=3/5,则cos2β=?设0<α<β<π/2,且cos(α+β)=-5/13,cos(α-β)=3/5,则cos2β=?

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设0<α<β<π/2,且cos(α+β)=-5/13,cos(α-β)=3/5,则cos2β=?设0<α<β<π/2,且cos(α+β)=-5/13,cos(α-β)=3/5,则cos2β=?

设0<α<β<π/2,且cos(α+β)=-5/13,cos(α-β)=3/5,则cos2β=?设0<α<β<π/2,且cos(α+β)=-5/13,cos(α-β)=3/5,则cos2β=?
设0<α<β<π/2,且cos(α+β)=-5/13,cos(α-β)=3/5,则cos2β=?
设0<α<β<π/2,且cos(α+β)=-5/13,cos(α-β)=3/5,则cos2β=?

设0<α<β<π/2,且cos(α+β)=-5/13,cos(α-β)=3/5,则cos2β=?设0<α<β<π/2,且cos(α+β)=-5/13,cos(α-β)=3/5,则cos2β=?
sin(a b)=12/13
sin(a-b)=-4/5
cos2b=cos[(a b)-(a-b)]=cos(a b)cos(a-b) sin(a b)sin(a-b)=-15/65-48/65=-63/65

0<α<β<π/2
0<α+β<π
-π/2<α-β<0
cos(α+β)=-5/13
sin(α+β)=12/13
cos(α-β)=3/5,
sin(α-β)=-4/5,
cos2β=cos[(α+β)-(α-β)]
=cos(α+β)cos(α-β)+sin(α+β)sin(α-β)
=-5/13*3/5+12/13*(-4/5)
=-15/65-48/65
=-63/65

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