Derivatives - Prove why (1-cos(h))/h = 0

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This proof is part of the video i did on why f'(sin(x)) = cos(x), i used this technique to prove that why sin(x) goes to cos(x) when derived but I didn't have enough time to show you why it is this way, so i made a separate video on it.
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whole video needs to be about 2 minutes

EzraSchroeder