#### Answer

$f(x)=\cos x$ and $a=\pi$

#### Work Step by Step

*By definition, the derivative of a function $f$ at a number $a$ is $$f'(a)=\lim\limits_{h\to0}\frac{f(a+h)-f(a)}{h}\hspace{0.5cm}(1)$$
Here we have
$$f'(a)=\lim\limits_{h\to0}\frac{\cos{(\pi+h)}+1}{h}$$
$$f'(a)=\lim\limits_{h\to0}\frac{\cos{(\pi+h)}-(-1)}{h}$$
$$f'(a)=\lim\limits_{h\to0}\frac{\cos{(\pi+h)}-\cos\pi}{h}$$
Now we match the formula found above with the formula of the derivative by definition.
We find that $a=\pi$, $f(a)=f(\pi)=\cos\pi$ and $f(x)=\cos x$