I was wondering how the Maclaurin series expansion for cotangent is derived using the Bernoulli numbers.

It is given as:

$\displaystyle \cot(x)=\sum^{\infty}_{n=0}\frac{(-1)^n2^{2n}B_{2n}x^{2n-1}}{(2n)!}$

I cannot normally find the Maclaurin expansion since $\displaystyle \cot(0)$ is undefined.

Could I derive this cotangent representation from the series representation of sine and cosine? Or tangent? If not, how would I?

Thank you very much.