Find the Maclaurin series for cos2(x)\cos^2(x)cos2(x).
1+∑n=1∞(−1)n22n−1x2n(2n)!1 + \sum_{n=1}^{\infty} \frac{(-1)^n 2^{2n-1} x^{2n}}{(2n)!}1+∑n=1∞(2n)!(−1)n22n−1x2n
∑n=0∞(−1)nx2n(2n)!\sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{(2n)!}∑n=0∞(2n)!(−1)nx2n
∑n=0∞(−1)n(2x)2n(2n)!\sum_{n=0}^{\infty} \frac{(-1)^n (2x)^{2n}}{(2n)!}∑n=0∞(2n)!(−1)n(2x)2n
1+∑n=0∞(−1)nx2n2(2n)!1 + \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{2(2n)!}1+∑n=0∞2(2n)!(−1)nx2n