cosπ/5 乘以cos2π/5等于多少

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cosπ/5 乘以cos2π/5等于多少
cosπ/5 乘以cos2π/5等于多少

cosπ/5 乘以cos2π/5等于多少
这一类题可用对称法：
设sinπ/5×sin2π/5=m
cosπ/5×cos2π/5＝n
则4mn=(2sinπ/5×cosπ/5)×(2sin2π/5×cos2π/5)
=sin2π/5×sin4π/5
= sin2π/5×sinπ/5=m
∴n=1/4
即cosπ/5×cos2π/5＝1/4

cosπ/5×cos2π/5
=(2sinπ/5×cosπ/5×2cos2π/5)/(4sinπ/5)
=(2sin2π/5×cos2π/5)/[4sin(π-π/5)]
=sin4π/5/(4sin4π/5)
=1/4

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