(-1)"r2n 1. For all z € R, cos I = L(2n)! -Σ n=0 (a) Find a power series that is equal to r cos(a) for all r ER. (b) Differentiate the series in (la) to find a power series that is equal to cos(r²) – 212 sin(r?) for all a E R. (c) Use the result in (1b) to prove that (-16)"(4n + 1) (2n)! cos(4) – 8 sin(4). n=0

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A: We will use Taylor's series expansion to find resulting power series.

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A: Let's replace x by x2 to obtain: Let's now expand up to four terms to get:

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A: We are authorized to solve only 1 question, please repost remaining questions

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A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

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