已知0<α<π/2<β<π,cos(β-π/4π)=1/3,sin(α+β)=4/5,sin2β=-7/9.cos(α+
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已知0<α<π/2<β<π,cos(β-π/4π)=1/3,sin(α+β)=4/5,sin2β=-7/9.cos(α+π/4)的值
![已知0<α<π/2<β<π,cos(β-π/4π)=1/3,sin(α+β)=4/5,sin2β=-7/9.cos(α+](/uploads/image/z/1727946-18-6.jpg?t=%E5%B7%B2%E7%9F%A50%EF%BC%9C%CE%B1%EF%BC%9C%CF%80%2F2%EF%BC%9C%CE%B2%EF%BC%9C%CF%80%2Ccos%EF%BC%88%CE%B2-%CF%80%2F4%CF%80%EF%BC%89%3D1%2F3%2Csin%EF%BC%88%CE%B1%2B%CE%B2%EF%BC%89%3D4%2F5%2Csin2%CE%B2%3D-7%2F9.cos%28%CE%B1%2B)
cos(β-π/4)=1/3 cos2(β-π/4)=2[cos(β-π/4)]^2-1=-7/9 cos(2β-π/2)=-7/9 cos(π/2-2β)=-7/9 sin2β=-7/9 cos(β-π/4)=1/3,sin(α+β)=4/5,0<α<π/2<β<π sin(β-π/4)=2√2/3 cos(α+β)=-3/5 cos(α+π/4)=cos[(α+β)+(π/4-β)] =cos(α+β)cos(π/4-β)-sin(α+β)sin(π/4-β) =cos(α+β)cos(β-π/4)+sin(α+β)sin(β-π/4) =(8√2-3)/15
已知0<α<π/2<β<π,cos(β-π/4π)=1/3,sin(α+β)=4/5,sin2β=-7/9.cos(α+
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