The document you uploaded contains a series of trigonometric problems written in Russian. Here’s a breakdown of the tasks:

1. Prove the identity
   $\frac{1 - \cos^2 \alpha}{\sin \alpha \cos \alpha} = \cot \alpha$
2. Find the values of $\sin \alpha$, $\tan \alpha$, and $\cot \alpha$, given $\cos \alpha = \frac{12}{13}$ and $\frac{\pi}{2} < \alpha < \frac{3\pi}{2}$.
3. Simplify the expression
   $\frac{9 - 9 \sin^2 \alpha}{3 \cos 2 \alpha}$
4. Simplify the expression:
   • a) $\frac{1 + \tan^2 \alpha}{1 + \sin \alpha}$
   • b) $\frac{1}{1 + \tan^2 \alpha} + \sin^2 \alpha$
5. Simplify the following expression: $\cot (\alpha - \alpha) + 1 = \frac{\cos (\alpha - \alpha) - \sin (\alpha - \alpha)}{\sin (\alpha - \alpha)}$

I'll help you solve each of these. Would you like to proceed with one at a time?