Partial Fractions Expansion of Cotangent/Proof 2

Proof
From the Euler Formula for Sine Function:
 * $\ds \frac {\sin x} x = \prod_{n \mathop = 1}^\infty \paren {1 - \frac {x^2} {n^2 \pi^2} }$

Taking the logarithm of both sides:


 * $\ds \ln \frac {\sin x} x = \sum_{n \mathop = 1}^\infty \map \ln {1 - \frac {x^2} {n^2 \pi^2} }$

and differentiating $x$:

Hence the result.