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Cosx Cos(x%p/2)=m在[0,2p]上有两个不同解A,B求m...

解:cosx cos(x-p/2)=m,即cosx (cosxcosp/2+sinx sin p/2)=m, cos²xcosp/2+sinx cosxsin p/2=m, 2cos²x+2sinx cosxtan p/2=2m/cosp/2, cos2x+sin2xtan p/2=2m/cosp/2-1, cos2x cosp/2 +sin2x sin p/2=2m-cosp/2, cos(2x-p/2)=2m...

令y=cos2x+cosx=2cos 2 x+cosx-1=2 (cosx+ 1 4 ) 2 - 9 8 .∵x∈[0, π 2 ],∴cosx∈[0,1].∴y=cos2x+cosx在x∈[0, π 2 ],上是增函数.故y max =-1,y min =2.又∵cos2x+cosx-m=0?m=cos2x+cosx∴m∈[-1,2].故选:C.

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