cosπ/9*cos2π/9*cos4π/9=?

cosπ/9*cos2π/9*cos4π/9=?
cosπ/9*cos2π/9*cos4π/9=?

cosπ/9*cos2π/9*cos4π/9=?
用因子8sinπ/9乘之,再除之得1/8

cosπ/9*cos2π/9*cos4π/9=(2*sinπ/9*cosπ/9*cos2π/9*cos4π/9)/2*sinπ/9
=2*sin2π/9*cos2π/9*cos4π/9)/2*2*sinπ/9
=2*sin4π/9*cos4π/9)/2*2*2*sinπ/9
...

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cosπ/9*cos2π/9*cos4π/9=(2*sinπ/9*cosπ/9*cos2π/9*cos4π/9)/2*sinπ/9
=2*sin2π/9*cos2π/9*cos4π/9)/2*2*sinπ/9
=2*sin4π/9*cos4π/9)/2*2*2*sinπ/9
=sin8π/9/(8sinπ/9)
=sinπ/9/(8sinπ/9)
=1/8

收起

1/8

-1/9^3