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ǰλãҳ >> ΪʲôCos3xCos2x=1/2(Cos5x+Cosx) >>

ΪʲôCos3xCos2x=1/2(Cos5x+Cosx)

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

e^(ix)=cosx+isinx e^(ix)+e^(i2x)+e^(i3x)++e*(inx)=(cosx+cos2x++cosnx)+i(sinx+sin2x++sinnx) =[e^(inx+ix) -e^(ix)]/[e^(ix)-1] һȺҶ˷ֳʵ鲿(ĸͷͬ (cosx-1)-isinxȺʵ鲿...

ֱ󵼾Ϳˣȶ벿3sin²xcosxcos2/xȻҰ벿󵼣sinηx1/2sin2/xȻӾͿˣѣͷûֽʣִֻˣ׵ĿԼ׷ʣϣԲɣ

: (1) S=sinx+sin3x+sin5x+......+sin(2n-1)x S=sin(2n-1)x+sin(2n-3)x+......+sinx ¶Ӧӵ(Ͳ): 2S=2sin(nx)cos(n-1)x+2sin(nx)cos(n-3)x+......+2sin(nx)cos(n-3)x+2sin(nx)cos(n-1)x S=sin(nx)[cos(n-1)x+cos(n-3)x+.......

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cosx*cos2x*cos4x = 2 sinx*cosx*cos2x*cos4x / (2sinx) = sin2x * cos2x *cos4x /(2sinx) =......= sin8x / (8sinx) cos3x*cos5x =(1/2) ( cos8x +cos2x) ԭʽ= (1/16) (1/sinx) [ sin8x cos8x + sin8xcos2x ] = (1/32) (1/sinx) [ sin16x + si...

cos(3/11) =cos(-8/11) =-cos(8/11) cos(5/11) =cos(16/11-) =-cos(16/11) ԣ cos(/11)cos(2/11)cos(3/11) cos(4/11)cos(5/11) =cos(/11)cos(2/11)cos(4/11) cos(8/11)cos(16/11) =32sin(/11)cos(/11)cos(2/...

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