cosx=1/7,cos(x-y)=13/14,0<y<x<π/2.求y
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cosx=1/7,cos(x-y)=13/14,0<y<x<π/2.求y
![cosx=1/7,cos(x-y)=13/14,0<y<x<π/2.求y](/uploads/image/z/19692359-71-9.jpg?t=cosx%3D1%2F7%2Ccos%28x-y%29%3D13%2F14%2C0%EF%BC%9Cy%EF%BC%9Cx%EF%BC%9C%CF%80%2F2.%E6%B1%82y)
由题意知:cosx=1/7 cos(x-y)=13/14
则通过计算可得:sinx=4√3/7 sin(x-y)=3√3/14
用余弦公式:cosx·cos(x-y)+sinx·sin(x-y)=cos[x-(x-y)]=cosy
即cosy=(1/7·13/14)+(4√3/7·3√3/14)=1/2
cosy=0.5 y=π/3
则通过计算可得:sinx=4√3/7 sin(x-y)=3√3/14
用余弦公式:cosx·cos(x-y)+sinx·sin(x-y)=cos[x-(x-y)]=cosy
即cosy=(1/7·13/14)+(4√3/7·3√3/14)=1/2
cosy=0.5 y=π/3
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