cosπ/5*cos2π/5的值等于 A1/4 B1/2 C2 D4

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cosπ/5*cos2π/5的值等于 A1/4 B1/2 C2 D4
cosπ/5*cos2π/5的值等于 A1/4 B1/2 C2 D4

cosπ/5*cos2π/5的值等于 A1/4 B1/2 C2 D4
选A 答案是1/4

cosπ/5*cos2π/5=2sinπ/5cosπ/5cosπ/5/(2sinπ/5)
=sin2π/5cosπ/5/(2sinπ/5)
=2sin2π/5cosπ/5/(4sinπ/5)
=sin4π/5/(4sinπ/5)
...

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cosπ/5*cos2π/5=2sinπ/5cosπ/5cosπ/5/(2sinπ/5)
=sin2π/5cosπ/5/(2sinπ/5)
=2sin2π/5cosπ/5/(4sinπ/5)
=sin4π/5/(4sinπ/5)
=sin(π-π/5)/(4sinπ/5)
=sinπ/5/(4sinπ/5)
=1/4
∴cosπ/5*cos2π/5的值等于 A1/4

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