求解cosπ⼀9cos2π⼀9cos(-23π⼀9)

2025-06-25 16:39:58
推荐回答(1个)
回答1:

=-1/8
利用3次正弦二倍角公式
cosπ/9cos2π/9cos(-23π/9)
=cosπ/9cos2π/9cos(-3π+4π/9)
=-cosπ/9cos2π/9cos4π/9
=-2sinπ/9cosπ/9cos2π/9cos4π/9/(2sinπ/9)
正弦二倍角
=-sin2π/9cos2π/9cos4π/9/(2sinπ/9)
=-2sin2π/9cos2π/9cos4π/9/(4sinπ/9)
正弦二倍角
=-sin4π/9cos4π/9/(4sinπ/9)
=-2sin4π/9cos4π/9/(8sinπ/9)
正弦二倍角
=-sin8π/9/(8sinπ/9)
=-sinπ/9/(8sinπ/9)
=-1/8
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