若sin(π/4-α)=3/5 sin(π/4+β)=12/130
问题描述：
若sin(π/4-α)=3/5 sin(π/4+β)=12/13
0
答
sin（α+β）=sin[(π/4+β)-(π/4-α)]=0.8x(12/13)-0.6x(5/13)=33/65
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COS（α+β）^2+sin（α+β）^2=1 所以COS（α+β）=56/65
答
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