Some non-trivial trigonometric identities from theta Functions

Resumo

It is always exciting to find relations between quantities that are not immediately and obviously related. In this regard, connecting theta functions and continued fractions with trigonometric functions is fascinating. Though trigonometric identities can also be established by elementary methods or by the help of software, the fact that they can be obtained by theta functions and continued fractions is intriguing. In the present research article, we deduce twelve trigonometric identities, using theta function identities listed by Ramanujan along with modular relations of few continued fractions.