已知0<x<45,sin(45-x)=5/13,求cos2x/cos(45+x)的值
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已知0<x<45,sin(45-x)=5/13,求cos2x/cos(45+x)的值
![已知0<x<45,sin(45-x)=5/13,求cos2x/cos(45+x)的值](/uploads/image/z/6109815-39-5.jpg?t=%E5%B7%B2%E7%9F%A50%EF%BC%9Cx%EF%BC%9C45%2Csin%2845%EF%BC%8Dx%29%EF%BC%9D5%2F13%2C%E6%B1%82cos2x%2Fcos%2845%EF%BC%8Bx%29%E7%9A%84%E5%80%BC)
cos(45+x)=sin[90-(45+x)]=sin(45-x)=5/13
sin(x+45)=√[1-cos^2(45+x)]=12/13
cos2x=cos^2x-sin^2x=(cosx+sinx)(cosx-sinx)
=1/2*sin(x+45)sin(45-x)=30/169
cos2x/cos(45+x)=(30/169)/(5/13)=6/13
sin(x+45)=√[1-cos^2(45+x)]=12/13
cos2x=cos^2x-sin^2x=(cosx+sinx)(cosx-sinx)
=1/2*sin(x+45)sin(45-x)=30/169
cos2x/cos(45+x)=(30/169)/(5/13)=6/13
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