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证明cos3x/cosx=2cos2x-1我自己做出来这些：=cos(2x+x)/cosx=(cos2xcosx-sin2xsinx)/cosx接下来该怎样?
题目详情
证明cos3x/cosx= 2cos2x-1
我自己做出来这些：
=cos(2x+x)/cos x
= (cos2xcosx-sin2xsinx)/cosx
接下来该怎样?
我自己做出来这些：
=cos(2x+x)/cos x
= (cos2xcosx-sin2xsinx)/cosx
接下来该怎样?
▼优质解答
答案和解析
cos3x
=cos(2x+x)
=cos2xcosx-sin2xsinx
=cos2xcosx-2sin²xcosx
=cos2xcosx-2(1-cos²x)cosx
=cos2xcosx-2cosx+2cos²x*cosx
=cos2xcosx-2cosx+(1+cos2x)cosx
=cos2xcosx-2cosx+cosx+cos2xcosx
=2cos2xcosx-cosx
=cos(2x+x)
=cos2xcosx-sin2xsinx
=cos2xcosx-2sin²xcosx
=cos2xcosx-2(1-cos²x)cosx
=cos2xcosx-2cosx+2cos²x*cosx
=cos2xcosx-2cosx+(1+cos2x)cosx
=cos2xcosx-2cosx+cosx+cos2xcosx
=2cos2xcosx-cosx
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