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Identifying a Function from a Maclaurin Series

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The Maclaurin series for a function ff is given by 1+x22!+x44!+x66!+⋯+x2n(2n)!+⋯\displaystyle 1 + \frac{x^2}{2!} + \frac{x^4}{4!} + \frac{x^6}{6!} + \cdots + \frac{x^{2n}}{(2n)!} + \cdots. Which of the following is an expression for f(x)f(x)?

A

12(ex+e−x)\frac{1}{2}(e^x + e^{-x})

B

cos⁡x\cos x

C

ex−sin⁡xe^x - \sin x

D

ex2e^{x^2}

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