求cos(2π/7)*cos(4π/7)*cos(6π/7)的值

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求cos(2π/7)*cos(4π/7)*cos(6π/7)的值

求cos(2π/7)*cos(4π/7)*cos(6π/7)的值
求cos(2π/7)*cos(4π/7)*cos(6π/7)的值

求cos(2π/7)*cos(4π/7)*cos(6π/7)的值
cos(2π/7)*cos(4π/7)*cos(6π/7)
= sin(2π/7)cos(2π/7)*cos(4π/7)*cos(6π/7)/sin(2π/7)
= 1/2 * sin(4π/7)cos(4π/7)*cos(6π/7)/sin(2π/7)
= 1/4 * sin(8π/7)*cos(6π/7)/sin(2π/7)
= -1/4 * sin(π/7)*cos(6π/7)/sin(2π/7)
= 1/4 * sin(π/7)*cos(π/7)/sin(2π/7)
= 1/8 * sin(2π/7)/sin(2π/7)
= 1/8

原=sin(2π7)*cos(2π/7)*cos(4π/7)*cos(6π/7)/sin(2π7)
=sin(4π/7)cos(4π/7)cos(6π/7)/2sin(2π7)
=sin(8π/7)cos(6π/7)/4sin(2π7)
=sin(π-8π/7)cos(6π/7)/4sin(2π7)
=sin(12π/7)/8sin(2π7)
=sin(2π-12π/7)/8sin(2π7)
=1/8