Use taylor series to verify

i know cos z =

and sin z =

and

but i cant get the steps to get there.

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- Sep 21st 2012, 10:59 AMlinalg123Taylor Series
Use taylor series to verify

i know cos z =

and sin z =

and

but i cant get the steps to get there. - Sep 21st 2012, 01:38 PMgirdavRe: Taylor Series
The sum for runs over even terms, and the corresponding one for of odd terms. So you just have to check that the coefficients of for odd/even indexes match.

- Sep 21st 2012, 07:00 PMjohnsomeoneRe: Taylor Series
Start with the series.

Break it down by what happens to that factor.

That will break the series into the sum of four series via the values of n mod 4.

Collect real and imaginary terms.

Simpify for the real and imaginary parts (this takes some care - gotta manipulate the series and their indices and such carefully).

That'll do it.