Answer
See proof below.
Work Step by Step
Given $f(x)=cos(x)$, we have $f(x+h)=cos(x+h)=cos(x)cos(h)-sin(x)sin(h)$, thus
$\frac{f(x+h)-f(x)}{h}=\frac{cos(x)cos(h)-sin(x)sin(h)-cos(x)}{h}
=\frac{cos(x)cos(h)-cos(x)}{h}-\frac{sin(x)sin(h)}{h}
=-cos(x)(\frac{1-cos(h)}{h})-sin(x)(\frac{sin(h)}{h})$
