Why is the taylor series for ln(x+1) so similar to the tailor series sin(x) or cos(x), yet the functions themselves are not at all?

Question

Why is the taylor series for ln(x+1) so similar to the tailor series sin(x) or cos(x), yet the functions themselves are not at all?

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Answer 1

All Taylor series are constructed using the same general form. The similarities that you recognise for the series of different functions are the “bones” of this generic shape. The differences in how these forms translate back to their function comes from whether different terms in the series cancel one another.