已知α,β∈(3/4π,π),sin(α+β)=-3/5,sin(β-π/4)+12/13,求cos(α+π/4)的值
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已知α,β∈(3/4π,π),sin(α+β)=-3/5,sin(β-π/4)+12/13,求cos(α+π/4)的值
抱歉是sin(β-π/4)=12/13
抱歉是sin(β-π/4)=12/13
![已知α,β∈(3/4π,π),sin(α+β)=-3/5,sin(β-π/4)+12/13,求cos(α+π/4)的值](/uploads/image/z/15280615-55-5.jpg?t=%E5%B7%B2%E7%9F%A5%CE%B1%2C%CE%B2%E2%88%88%283%2F4%CF%80%2C%CF%80%29%2Csin%28%CE%B1%2B%CE%B2%29%3D-3%2F5%2Csin%28%CE%B2-%CF%80%2F4%29%2B12%2F13%2C%E6%B1%82cos%28%CE%B1%2B%CF%80%2F4%29%E7%9A%84%E5%80%BC)
α,β∈(3/4π,π),sin(α+β)=-3/5,sin(β-π/4)+12/13
cos(a+b)=4/5,cos(b-pai/4)=5/13
cos(α+π/4)
=cos(a+b-(b-pai/4)
=cos(a+b)c0s(b-pai/4)+sin(a+b)sin(b-pai/4)
=4/5*5/13-(-3/5)*(12/13)
=56/65
cos(a+b)=4/5,cos(b-pai/4)=5/13
cos(α+π/4)
=cos(a+b-(b-pai/4)
=cos(a+b)c0s(b-pai/4)+sin(a+b)sin(b-pai/4)
=4/5*5/13-(-3/5)*(12/13)
=56/65
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