Find difference quotient for $f(x) = \sin x$ I need to use the different quotient:
$\frac{f(x+h)-f(x)}{h}$
to show that
$f(x) = \sin(x)$
simplifies to
$\cos(x) \frac{\sin(h)}{h} + \sin(x)  \frac{\cos(h)-1}{h}$
How do I do that? I already have, working from the start point,
$\frac{\sin(x)\cos(h)+\cos(x)\sin(h)-\sin(x)}{h}$
but I don't know where to go from there. Thank you!
EDIT:
Following a hint from the first comment, I now have
$\frac{(\sin(x))(\cos(h) - 1)}{h} + \frac{\cos(x)\sin(h)}{h}$

Things are much easier if we choose to use Prosthaphaeresis Formula,
$$\sin(x+h)-\sin x=2\sin\dfrac h2\cos\dfrac{2x+h}2$$
and use $\lim_{u\to0}\dfrac{\sin u}u=1$
