求sin2/7π+sin3/7π-sinπ/7的值(根号7)/2,怎么算的

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求sin2/7π+sin3/7π-sinπ/7的值(根号7)/2,怎么算的求sin2/7π+sin3/7π-sinπ/7的值(根号7)/2,怎么算的求sin2/7π+sin3/7π-sinπ/7的值(

求sin2/7π+sin3/7π-sinπ/7的值(根号7)/2,怎么算的
求sin2/7π+sin3/7π-sinπ/7的值
(根号7)/2,怎么算的

求sin2/7π+sin3/7π-sinπ/7的值(根号7)/2,怎么算的
sin(2π/7)+sin(3π/7)-sin(π/7)=sin(5π/14-π/14)+sin(5π/14+π/14)-sinπ/7
=sin5π/14cosπ/14-cos5π/14sinπ/14+sin5π/14cosπ/14+cos5π/14sinπ/14-sinπ/7
=2sin5π/14cosπ/14-sinπ/7
=2cos(2π/14)cos(π/14)-sin(π/7)=2sin(π/14)cos(π/14)cos(2π/14)/sin(π/14)-sin(π/7)
=sin(2π/14)cos(2π/14)/sin(π/14)-sin(π/7)=(1/2)sin(4π/14)/sin(π/14)-sin(π/7)
=(1/2)sin(2π/7)/sin(π/14)-sin(π/7)=(1/2)sin(2π/7)/cos(6π/14)-sin(π/7)
=(-1/2)sin(2π/7)/cos(2π/7)-sin(π/7)

综上所述,2sinα/(cosα-sinα-cos3α+sin3α)=1/(sin(2α)+cos(2α))=1/(-24/25-7/25)=-25/31。最后附上和差化积公式: sina+sinb=