已知a*sin(x-y)=sinx-siny.其中a>1.求cos(x-y)的取值范围(要求含有a).
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已知a*sin(x-y)=sinx-siny.其中a>1.
求cos(x-y)的取值范围(要求含有a).
-1
由已知得:
a*sin(x-y)*cos(x-y)=cos(x-y)*(sinx-siny)
所以cos(x-y)={a*sin(x-y)*cos(x-y)}/(sinx-siny)
={a*sin(2x-2y)}/{2*a*sin(x-y)}
=(sin2x-sin2...
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由已知得:
a*sin(x-y)*cos(x-y)=cos(x-y)*(sinx-siny)
所以cos(x-y)={a*sin(x-y)*cos(x-y)}/(sinx-siny)
={a*sin(2x-2y)}/{2*a*sin(x-y)}
=(sin2x-sin2y)/{2*a*sin(x-y)}
因为sin2x-sin2y=sin{(2x-2y)/2+(2x+2y)}-sin{(2x+2y)/2-(2x-2y)/2}
=2sin(x-y)cos(x+y)
所以cos(x-y)=2sin(x-y)cos(x+y)/{2a*sin(x-y)}
=cos(x+y)/a
因为x,y取值为R
所以-1/a
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