当X趋向于0时 1-cosx cos2x cos3x与ax n为等价无穷小 求n a,当x趋向于无穷时cosx等于多少

1-cosxcos2xcos3x=1-cosx(1-2sin^2x)(cosxcos2x-sinxsin2x)

=1-cosx(1-2sin^2x)[cosx(1-2sin^2x)-2sin^2xcosx]

=1-cos^2x(1-2sin^2x)(1-4sin^2x)

=1-(1-sin^2x)(1-2sin^2x)(1-4sin^2x)

=8sin^6x-14sin^4x+7sin^2x，

由于sinx与x为等阶无穷小，而sin^6x和sin^4x相对于sin^2x是高阶无穷小，

因此8sin^6x-14sin^4x+7sin^2x与7x^2为等阶无穷小，即n=2，a=7。