求cos20×cos40×cos60×cos80

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求cos20×cos40×cos60×cos80求cos20×cos40×cos60×cos80求cos20×cos40×cos60×cos80cos20×cos40×cos60×cos80=sin2

求cos20×cos40×cos60×cos80
求cos20×cos40×cos60×cos80

求cos20×cos40×cos60×cos80
cos20×cos40×cos60×cos80
=sin20×cos20×cos40×cos60×cos80/sin20
=sin40×cos40×cos60×cos80/2sin20
=sin80×cos60×cos80/4sin20
=sin160×cos60/8sin20
=sin20×cos60/8sin20
=cos60/8=1/16
因为cos60=1/2,逐步利用倍角公式