化简cosπ/9*cos2π/9*cos3π/9*cos4π/9
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k/k法
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.
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.
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