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

1 Answer
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