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ǰλãҳ >> 2Cos2xCosx=Cosx+Cos3xΪʲô? >>

2Cos2xCosx=Cosx+Cos3xΪʲô?

Ͳʽ 2cosAcosB = cos(A+B)+cos(A-B) A=2xB=x뼴

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cos2x-x+cos2x+x =cos2xcosx+sin2xsinx+cos2xcosx-sin2xsinx =2cos2xcosx

ΪߵĺʵұһԻΪʵĻֻҪȡexp(ix/2)exp(inx/2)֮ľͿˡϲòͬᵼȡexp(-ix/2)exp(-inx/2)

ԣΪcos2a=cos²a-sin²a=1-2sin²a=2cos²a-1 ͬcos2x=1-2sin²x=2cos²x-1 cosxcos2x=2cos³x-cosx

ͲʽڵĽ̲Ѿɾˣ ˼· ҵ x3x ƽֵ2x ƽֵ 2x ƽֵΪߣԭĽǵʽɵߵĽ x,2x, ˼·ڵȲУ cosx+cos3x=cos(2x-x)+cos(2x+x) =[cos2xc...

⣺ ǺͲʽתġ£ cos(+)=coscos-sinsin cos(-)=coscos+sinsin ʽӣ cos(+)+cos(-) = 2coscos coscos=1/2[cos(+)+cos(-)] Ӷ cosx/2cos3x/2=1/2[cos(x/2+3x/2)+cos(x/...

ΪcosX- cos3X =cos(2x-x)-cos(2x+x) =cos2xcosx+sin2xsinx -(cos2xcosx-sin2xsinx) =2sin2xsinx

cos2xcos3x =cos3xcos2x =(1/2){cos(3x+2x)+cos(3x-2x)} =1/2(cos5x+cosx)

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