Question

急急急，学霸快快快

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Answer 1

Answer 2

cosπ/7*cos2π/7*cos3π/7

=-cosπ/7*cos2π/7*cos4π/7
=-sin(π/7)*cos(π/7)*cos(2π/7)*cos(4π/7)/sin(π/7)
=-(1/2)sin(2π/7)*cos(2π/7)*cos(4π/7)/sin(π/7)
=-(1/4)sin(4π/7)*cos(4π/7)/sin(π/7)

=-(1/8)cos(8π/7)/sin(π/7)
因为 sin(8π/7)=sin(π+π/7)=-sin(π/7)
=1/8

Answer 3

用和差化积公式把后面两项化为第一项的形式试试吧。

Answer 4

cosπ/7cos2π/7cos3π/7
=2sinπ/7cosπ/7cos2π/7cos3π/7/2sinπ/7
=sin2π/7cos2π/7[-cos(π-3π/7)]/2sinπ/7
=-sin4π/7cos4π/7/4sinπ/7
=-sin8π/7/8sinπ/7
=sinπ/7/8sinπ/7
=1/8

追答

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