I understand everything in the proof except the(adsbygoogle = window.adsbygoogle || []).push({}); laststep I have written here. What comes after, I understand.

How is it that the cosine and sine are able to be factored out of the fraction? That one step gets me. I was never too good with my trig, and have finally gotten a decent grasp of it, but this one befuddles me.

Prove: [itex]\frac{d}{dx}[sin (x)] = cos (x) [/itex]

[itex] \frac{d}{dx}[sin (x)] = \lim_{\Delta x \to 0}\frac{sin (x) cos (\Delta x) + cos (x) sin (\Delta x) - sin (x)}{\Delta x}[/itex]

[itex] = \lim_{\Delta x \to 0}\frac{cos(x) sin (\Delta x) - (sin (x)) (1- cos(\Delta x))}{\Delta x}[/itex]

[itex] = \lim_{\Delta x \to 0} \Bigg(cos(x) \frac {sin (\Delta x)} {\Delta x} - sin(x) \frac {(1-cos(\Delta x)} {\Delta x}\Bigg) [/itex]

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# Help with 1 step in proof of d/dx sin x = cos x

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