Use the Taylor series given in Key Idea 8.8.1 to verify the given identity:
\[cos(-x) = cox(x)\] We are given that:
\[cos(x) = \sum_{n=0}^{\infty} (-1)^{n}\frac{x^{2n}}{(2n)!}\]
and the first few terms are:
\[1 - \frac{x^{2}}{2!} + \frac{x^{4}}{4!} - \frac{x^{6}}{6!} + ...\]
The first few terms of cos(-x) are then:
\[1 - \frac{(-x)^{2}}{2!} + \frac{(-x)^{4}}{4!} - \frac{(-x)^{6}}{6!} + ...\]
\[ = 1 - \frac{x^{2}}{2!} + \frac{x^{4}}{4!} - \frac{x^{6}}{6!} + ...\]
Which is obviously equal to those of \(cos(x)\).