The difference quotient is:

$\displaystyle \frac{d}{dx}sin(x) = \lim \Delta x\rightarrow 0=\frac{sin(x+\Delta x)-sin(x)}{\Delta x}$

which converts to:

$\displaystyle =\lim \Delta x\rightarrow 0\frac{sin(x)cos\Delta x+cos(x)sin(\Delta x)-sin(x)}{\Delta x}$

The above I understand. The below step is supposed to be an algebraic rearrangement of the above:

$\displaystyle \frac{d}{dx}sin(x)=\lim \Delta x\rightarrow 0[cos(x)(\frac{sin(\Delta x)}{\Delta x})-sin(x)(\frac{1-cos(\Delta x)}{\Delta x})]$

I am wondering how things were changed to the step above. I am not seeing it right now.

Thanks in advance...