求值:cos(2pai/7)+cos(4pai/7)+cos(6pai/7)

问题描述:

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