Prove That ?? #Cos((3π)/13 )+ Cos((5π)/13) - 2 Cos((9π)/13) Cos((12π)/13 )= 0#

1 Answer
P dilip_k
May 16, 2018

#LHS=Cos((3π)/13 )+ Cos((5π)/13) - 2 Cos((9π)/13) Cos((12π)/13 )#

#=Cos((3π)/13 )+ Cos((5π)/13) - [ Cos((21π)/13) +Cos((3π)/13) ]#
#=Cos((3π)/13 )+ Cos((5π)/13) - [ Cos(2pi-(5π)/13) +Cos((3π)/13) ]#

#=Cos((3π)/13 )+ Cos((5π)/13) - Cos((5π)/13) -Cos((3π)/13) #

#= 0=RHS#

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