分类：教育/科学-学习帮助
问题：三角函数题012已知α∈(π/4,3π/4),β∈(0,π/4) 
已知α∈(π/4,3π/4),β∈(0,π/4)且c(π/4-α)=3/5,sin(3π/4+β)=5/13,求sin(α+β)的值.
回答：α∈(π/4,3π/4),π/4-α∈(-π/2,0), ∴ sin(π/4-α)=-4/5.β∈(0,π/4),3π/4+β∈(3π/4,π),cos(3π/4+β)=-12/13,sin(α+β)=-cos[(3π/4+β)-(π/4-α)]=sin(3π/4+β)sin(π/4-α)-cos(3π/4+β)cos(π/4-α)=5/13×(-4/5)-(3/5)×(-12/13)=16/65