For the limit: $$\displaystyle\lim_{x\to\frac{\pi}{4}} \frac{1}{\cot{x}-1}$$ the one sided limits are $\displaystyle\lim_{x\to\frac{\pi}{4}^{-}} \frac{1}{\cot{x}-1}=\infty$
and $\displaystyle\lim_{x\to\frac{\pi}{4}^{+}} \frac{1}{\cot{x}-1}=-\infty$.
Why? should they not be both $+\infty$? I dont really understand how to evaluate limits in which i arrive to $\frac10$