作业帮求值cosπ/5cos2π/5cos4π/5cos8π/5
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求值cosπ/5cos2π/5cos4π/5cos8π/5
求值cosπ/5cos2π/5cos4π/5cos8π/5
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
cos(π/5)cos(2π/5)cos(4π/5)cos(8π/5)
＝(1/2)·(2sin(π/5)cos(π/5))cos(2π/5)cos(4π/5)cos(8π/5)·(1/sin(π/5))
＝(1/2)·sin(2π/5)cos(2π/5)cos(4π/5)cos(8π/5)·(1/sin(π/5))
＝(1/4)sin(4π/5)cos(4π/5)cos(...
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cos(π/5)cos(2π/5)cos(4π/5)cos(8π/5)
＝(1/2)·(2sin(π/5)cos(π/5))cos(2π/5)cos(4π/5)cos(8π/5)·(1/sin(π/5))
＝(1/2)·sin(2π/5)cos(2π/5)cos(4π/5)cos(8π/5)·(1/sin(π/5))
＝(1/4)sin(4π/5)cos(4π/5)cos(8π/5)·(1/sin(π/5))
＝(1/8)sin(8π/5)cos(8π/5)·(1/sin(π/5))
＝(1/16)sin(16π/5)/sin(π/5)
＝(1/16)·(-sin(π/5))/sin(π/5)
＝-1/16.
注：sin(16π/5)＝sin[3π+(π/5)]＝-sin(π/5).
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