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Assume that angle $x$ is small, using small angle approximation,



and $\tan(x)=x$.

I am able to justify the first two using Maclaurin's Theorem but not the last one. How do we justify the last one?

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Hint : Taylor formula for tan(x) – Peter Dec 9 '13 at 9:19
We have a series expansion for $tan(x)$ also when $x$ is small , higher powers get neglected only first power will remain and hence it $x$ – AbKDs Dec 9 '13 at 9:20

Hint: for small $x$, $\frac{1}{\cos{x}}\approx\frac{1}{1-\frac{x^2}{2}}\approx 1+\frac{x^2}{2}$

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