cos(π/3+α)=-3/5,sin(2π/3-β)=5/13,且0

cos(π/3+α)=-3/5,sin(2π/3-β)=5/13,且0
cos(π/3+α)=-3/5,sin(2π/3-β)=5/13,且0

cos(π/3+α)=-3/5,sin(2π/3-β)=5/13,且0
cos(π/3+a)=-3/5,因为0

cos(β-α)=-cos(π-(β-α))=-cos((2π/3-β)+(π/3+α))=-cos((2π/3-β)cos(π/3+α)+sin((2π/3-β)sin(π/3+α)；
π/3<π/3+α<5π/6，-π/3<2π/3-β<π/6，所以sin(π/3+α)=4/5，cos(2π/3-β)=12/13；
所以cos(β-α)=36/65+20/65=56/65