C(N,1)COSX+C(N,2)COS2X+-----+C(N,N)COSNX
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C(N,1)COSX+C(N,2)COS2X+-----+C(N,N)COSNX
设 C(N,1)COSX+C(N,2)COS2X+-----+C(N,N)COSNX=A ,
C(N,1)sinX+C(N,2)sin2X+-----+C(N,N)sinNX=B
则 A+Bi= C(N,1)e^iX+C(N,2)e^2iX+-----+C(N,N)e^Nix
=(1+cosx+isinx)^n-1=[2cos^20.5x+2isin0.5xcos0.5x]^n-1
=2^ncos^n0.5x[cos0.5nx+isin0.5nx]-1
所以 A=2^ncos^n0.5xcos0.5nx-1,B=2^ncos^n0.5xsin0.5nx
C(N,1)sinX+C(N,2)sin2X+-----+C(N,N)sinNX=B
则 A+Bi= C(N,1)e^iX+C(N,2)e^2iX+-----+C(N,N)e^Nix
=(1+cosx+isinx)^n-1=[2cos^20.5x+2isin0.5xcos0.5x]^n-1
=2^ncos^n0.5x[cos0.5nx+isin0.5nx]-1
所以 A=2^ncos^n0.5xcos0.5nx-1,B=2^ncos^n0.5xsin0.5nx
C(N,1)COSX+C(N,2)COS2X+-----+C(N,N)COSNX
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