急、COSπ/9COS2π/9COS4π/9=?同样,

同尘2022-10-04 11:39:542条回答

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wanxuchu 共回答了24个问题 | 采纳率95.8%: π/9=20°2π/9=40°4π/9=80°
cos20cos40cos80
=sin20cos20cos40cos80/sin20
=1/2*sin40cos40cos80/sin20
=1/4*sin80cos80/sin20
=1/8*sin160/sin20
=1/8*sin20/sin20
=1/8; 1年前

kickcc 共回答了61个问题 | 采纳率: 利用2倍角公式
cosπ/9*cos2π/9*cos4π/9
=[sinπ/9*cosπ/9*cos2π/9*cos4π/9]/sinπ/9
=[1/2sin2π/9*cos2π/9*cos4π/9]/sinπ/9
=[1/4sin4π/9*cos4π/9]/sinπ/9
=[1/8sin8π/9]/sinπ/9
=[1/8sinπ/9]/[sinπ/9]
=1/8; 1年前

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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 )
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=(sin8π/9 cos3π/9)/(8sinπ/9 )
=(cosπ/3)/8
=1/16.

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