Derving two general formulae of trigonometric series found in "Subsidium Calculi Sinuum" of Euler

 In this post, with the help of A-Student, I have proved the two trigonometrical formulae of Euler. In this thread, I will prove 2 more general formlae found in his paper "Subsidium Calculi Sinuum" (Contribution to the calculation of sine) by Euler.

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Ramanujan, the "Euler" of 20th century

      The first time I heard of the name Ramanujan was in 2017. At that time, I was wondering on the internet, searching information about i...