The Maclaurin series for $\cos x$ is given by:
\[\cos x = 1 - \frac{x^{2}}{2!} + \frac{x^{4}}{4!} - \frac{x^{6}}{6!} + \cdots\]
Substituting $x^{2}$ for $x$ in the series, we get:
\[\cos x^{2} = 1 - \frac{x^{4}}{2!} + \frac{x^{8}}{4!} - \frac{x^{12}}{6!} +
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