
Expand tan(x+pi/4)
What is the quickest method to do this Taylor expansion for the first three terms? Somebody previously suggested doing the expansion for tan(x) and then substituting in (x + pi/4) but if I do that I get the following working and run into problems:
http://latex.codecogs.com/gif.latex?...20+%20...%20=?
Thanks in advance.

First of all, the series for $\displaystyle tan$ is incorrect.
Substitution will give you the Taylor series about $\displaystyle \pi/4$. Is it the Maclaurin series that you're looking for? If so, you need to differentiate and evaluation at 0.

1 Attachment(s)
$\displaystyle f(x) = f(c) + f'(c)(x  c) + \dfrac{f''(c)(xc)^2}{2!} + ...$
$\displaystyle f(x) = \tan{x}$ centered at $\displaystyle c = \frac{\pi}{4} ...$
$\displaystyle f(x) = f\left(\frac{\pi}{4}\right) + f'\left(\frac{\pi}{4}\right)\left(x  \frac{\pi}{4}\right) + \dfrac{f''\left(\frac{\pi}{4}\right)\left(x  \frac{\pi}{4}\right)^2}{2!} + ...$
$\displaystyle \tan{x} = 1 + 2\left(x  \frac{\pi}{4}\right) + 2\left(x  \frac{\pi}{4}\right)^2 + ...$
$\displaystyle \tan\left(x + \frac{\pi}{4}\right) = 1 + 2x + 2x^2 + ...$
