Question

cosπ/9×cos2π/9×cos3π/9×cos4π/9 求解答详细过程

Answer 1

1/16。
解：cosπ/9×cos2π/9×cos3π/9×cos4π/9
=(2sinπ/9xcosπ/9×cos2π/9×cos3π/9×cos4π/9)/2sinπ/9
=(sin2π/9xcos2π/9×cos3π/9×cos4π/9)/2sinπ/9
=(2sin2π/9xcos2π/9×cos3π/9×cos4π/9)/4sinπ/9
=(sin4π/9xcos3π/9×cos4π/9)/4sinπ/9
=(sin4π/9×cos4π/9xcosπ/3)/4sinπ/9
=(2sin4π/9×cos4π/9xcosπ/3)/8sinπ/9
=(sin8π/9xcosπ/3)/8sinπ/9
=(sinπ/9xcosπ/3)/8sinπ/9
=(cosπ/3)/8
=1/2x1/8=1/16
1),先乘以2sinπ/9,再除以2sinπ/9，
2),使分子出现2sinπ/9cosπ/9,
3),逆用公式sin2a=2sinacosa

Answer 2

cosπ/9*cos2π/9*cos3π/9*cos4π/9
＝[(2sinπ/9 cosπ/9)*cos2π/9*cos3π/9*cos4π/9]/(2sinπ/9 )
=[(2sin2π/9 cos2π/9)*cos3π/9*cos4π/9]/(4sinπ/9 )
=[(2sin4π/9 cos4π/9)*cos3π/9]/(8sinπ/9 )
=(sin8π/9 cos3π/9)/(8sinπ/9 )
=(cosπ/3)/8
=1/16.

Answer 3

cosπ/9×cos2π/9×cos3π/9×cos4π/9
=[2sinπ/9cosπ/9×cos2π/9×cos3π/9×cos4π/9]/2sinπ/9
=[2sin2π/9×cos2π/9×cos3π/9×cos4π/9]/4sinπ/9
=[sin4π/9×cos3π/9×cos4π/9]/4sinπ/9
=[2sin4π/9×cos4π/9×cos3π/9]/8sinπ/9
=[sin8π/9×cos3π/9]/8sinπ/9
=cos3π/9/8
=cosπ/3/8
=1/16

Answer 4