求值:cos(2pai/7)+cos(4pai/7)+cos(6pai/7)pai打不出,不好意思

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求值:cos(2pai/7)+cos(4pai/7)+cos(6pai/7)pai打不出,不好意思
求值:cos(2pai/7)+cos(4pai/7)+cos(6pai/7)
pai打不出,不好意思

求值:cos(2pai/7)+cos(4pai/7)+cos(6pai/7)pai打不出,不好意思
cos(2π/7)+cos(4π/7)+cos(6π/7)
=[sin(2π/7)cos(2π/7)+sin(2π/7)cos(4π/7)+sin(2π/7)cos(6π/7)]/sin(2π/7)
(下面用积化和差)
=1/2[sin(4π/7)+sin(6π/7)-sin(2π/7)+sin(8π/7)-sin(4π/7)]/sin(2π/7)
=1/2[sin(6π/7)-sin(2π/7)+sin(8π/7)]/sin(2π/7)
=1/2[-sin(2π/7)]/sin(2π/7)
=-1/2

COS=70

把前面的2*π/7写成4*π/7-2*π/7后面的6*π/7写成4*π/7+2*π/7,然后展开,应该就可以做出来了