求cosπ/9*cos2π/9*cos4π/9的值 - 知识问答

求cosπ/9*cos2π/9*cos4π/9的值

3个回答

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

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