Wednesday, 31 August 2016

geometry - How to prove cosleft(piover7right)cosleft(2piover7right)+cosleft(3piover7right)=cosleft(piover3right)



Is there an easy way to prove the identity?





cos(π7)cos(2π7)+cos(3π7)=cos(π3)




While solving one question, I am stuck, which looks obvious but without any feasible way to approach.



Few observations, not sure if it would help
π7+3π72=2π7π7+3π7+2π7=ππ7


Answer



Yes, This problem in 1963 IMO.http://www.artofproblemsolving.com/Forum/viewtopic.php?p=346908&sid=8ad587e18dd5fa9dd5456496a8daadfd#p346908


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