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求值cosπ/5cos2π/5cos4π/5cos8π/5

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求值cosπ/5cos2π/5cos4π/5cos8π/5
求值cosπ/5cos2π/5cos4π/5cos8π/5
利用正弦二倍角公式
cosπ/5cos2π/5cos4π/5cos8π/5
=2sinπ/5cosπ/5cos2π/5cos4π/5cos8π/5/(2sinπ/5)
=sin2π/5cos2π/5cos4π/5cos8π/5/(2sinπ/5)
=2sin2π/5cos2π/5cos4π/5cos8π/5/(4sinπ/5)
=sin4π/5cos4π/5cos8π/5/(4sinπ/5)
=2sin4π/5cos4π/5cos8π/5/(8sinπ/5)
=sin8π/5cos8π/5/(8sinπ/5)
=2sin8π/5cos8π/5/(16sinπ/5)
=sin16π/5/(16sinπ/5)
=sin(3π+π/5)/(16sinπ/5)
=-sinπ/5/(16sinπ/5)
=-1/16
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