Answer
$f(x)$ = $cos(x)$
$a = \pi$
Work Step by Step
The form of the equation given resembles the form
$\lim\limits_{h \to 0}$ $\frac{f(h+a) - f(a)}{h}$
Since $\pi$ is being added to $x$, $a = \pi$. We also see that $f(a + h) $ = $cos(\pi + h)$, so our function $f(x)$ must be $cos(x)$.
We can check our answer by looking at the right term in the numerator, which would be $f(a)$ = $f(\pi)$ = $cos(\pi)$ = -1. Since the right term is subtracted, we would be left with -(-1) or 1.
Thus, $f(x)$ = $cos(x)$ and $a = \pi$
