若sin(π/4-α)=3/5 sin(π/4+β)=12/130

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若sin(π/4-α)=3/5 sin(π/4+β)=12/130

若sin(π/4-α)=3/5 sin(π/4+β)=12/130
若sin(π/4-α)=3/5 sin(π/4+β)=12/13
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若sin(π/4-α)=3/5 sin(π/4+β)=12/130
sin(3π/4+β-π/4+α)=sin(π/2+α+β)=-cos(α+β)
cos(3π/4+β)=-12/13
cos(π/4-α)=3/5
sin(3π/4+β-π/4+α)
=cos(π/4-α)sin(3π/4+β)-sin(π/4-α)cos(3π/4+β)
=(5/13)*(3/5)-(-4/5)*(-12/13)
=-33/65

sin(α+β)=sin[(π/4+β)-(π/4-α)]=0.8x(12/13)-0.6x(5/13)=33/65
0<α<π/4 0<β<π/4 0<α+β<π/2 COS(α+β)>0
COS(α+β)^2+sin(α+β)^2=1 所以COS(α+β)=56/65