Identities involving trigonometric functions and Bernoulli numbers

The main purpose of this paper is using the elementary method and the properties of trigonometric functions to study the computational problem of one kind trigonometric sums, and give some interesting identities involving sin (x), cos (x), tan (x), cot(x), Bernoulli numbers and Dirichlet L-functions. As a result, we obtain a relationship between the summation of cot(x) with character and Dirichlet L-function.