# Taylor & MacLaurin series

I have a problem that I can not understand at all. I know how to calculate taylor/macLaurin for $\cos x$, $\sin x$ and $e^x$ etc. However when I have for example: $\sin x \cos x$ or $\sin x + \cos x$ or $\sin x-\cos x$ I have no idea how am I supposed to calculate this. Could you give me some hints on how to do such thing?

• Write down the series for $\sin x$ and $\cos x$, then multiply them out, add them term-by-term, or subtract them term-by-term as needed. – Antonio Vargas Feb 8 '14 at 15:03

If you are interested in this type of functions, then it is useful to convert the functions as linear combinations of the functions $e^{iax}$ and then find the the $n$th derivative which you need to construct Taylor series. If you are interested in more general techniques, see section 6.