ZA-SAMO 2008 Problem 6

Find all function pairs $(f,g)$ where each $f$ and $g$ is a function defined on the integers and with values, such that, for all integers $a$ and $b$ , $$f(a+b)=f(a)g(b)+g(a)f(b) g(a+b)=g(a)g(b)-f(a)f(b).$$