I am trying to evaluate lim of f(x)=COTx as x approaches $\displaystyle \frac{pi}{4}$ using the formula f'(a)=$\displaystyle \frac{cotx-cota}{x- a}$ and a=$\displaystyle \frac{pi}{4}}$

so..

$\displaystyle \frac{cotx-1}{x- \frac{pi}{4}}$

The answer is is suppose to be -2. How can I find the steps to get to -2?

I am sure I need to somehow use the trig limits $\displaystyle \frac{sinx}{x}=1$ and $\displaystyle \frac{cosx-1}{x}=0 $

I start off like this, i suppose

$\displaystyle \frac{\frac{cos}{sin}-1}{x- \frac{pi}{4}}$