Answer
See below.
Work Step by Step
Step 1. Given $f(x)=cos(x)$, we have $f(x+h)=cos(x+h)=cos(x)cos(h)-sin(x)sin(h)$
Step 2. We have $\frac{f(x+h)-f(x)}{h}=\frac{cos(x)cos(h)-sin(x)sin(h)-cos(x)}{h}=\frac{-sin(x)sin(h)-cos(x)(1-cos(h))}{h}=-sin(x)\cdot\frac{sin(h)}{h}-cos(x)\cdot\frac{1-cos(h)}{h}$
