Question #11ee3

1 Answer
Feb 4, 2018

Let

#p=cos ((2π)/7) + cos( (4π)/7) + cos ((6π)/7)#

#=>2p sin((2pi)/7)=2sin((2pi)/7)cos ((2π)/7) +2sin((2pi)/7)cos( (4π)/7) +2sin((2pi)/7)cos ((6π)/7)#

#=cancelsin((4pi)/7)+sin((6pi)/7)-sin((2 pi)/7)+sin((8pi)/7)-cancelsin((4pi)/7)#

#=sin(pi-pi/7)-sin((2 pi)/7)+sin(pi+pi/7)#

#=cancelsin(pi/7)-sin((2 pi)/7)-cancelsin(pi/7)#

#=>p=-sin((2pi)/7)/(2sin((2pi)/7))=-1/2#