Partial Fractions Expansion of Cotangent/Proof 2

Proof
From the Euler Formula for Sine Function:
 * $\displaystyle \frac {\sin x} x = \prod_{n \mathop = 1}^\infty \left({1 - \frac {x^2} {n^2 \pi^2}}\right)$

Taking the logarithm of both sides:


 * $\displaystyle \ln \frac {\sin x} x = \sum_{n \mathop = 1}^\infty \ln \left({1 - \frac {x^2} {n^2 \pi^2}}\right)$

and differentiating $x$:

Hence the result.