Question

cosπ/7cos2π/7cos3π/7=?

有解题过程

Answer 1

原式=sinπ/7*cosπ/7*cos2π/7*cos3π/7/sinπ/7
=2sinπ/7*cosπ/7*cos2π/7*cos(π-4π/7)/2sinπ/7
=sin2π/7*cos2π/7*(-cos4π/7)/2sinπ/7
=-2sin2π/7*cos2π/7*cos4π/7/4sinπ/7
=-sin4π/7*cos4π/7/4sinπ/7
=-2sin4π/7*cos4π/7/8sinπ/7
=-sin8π/7/8sinπ/7
=sinπ/7/8sinπ/7
=1/8

Answer 2

cosπ/7cos2π/7cos3π/7
=cos(π/7)cos(2π/7)cos(π/2-π/7)
=cos(π/7)cos(2π/7)sin(π/7)
=sin(2π/7)cos(2π/7)/2
=sin(4π/7)/4
运用sin2a=2sinacosa