Chapter 10: Infinite Sequences and Series - Section 10.10 - The Binomial Series and Applications of Taylor Series - Exercises 10.10 - Page 633: 48

$$\cos (3x)$$

Recall the Taylor series for $\cos x=1-\dfrac{ x^2}{2!}+\dfrac{x^4}{4!}-....$ Now, $=1-\dfrac{3^2 \cdot x^2}{2!}+\dfrac{3^4 \cdot x^4}{4!} - \dfrac{3^6 \cdot x^6}{6!}+.....$ or, $=1-\dfrac{1}{2!}(3x)^2+( \dfrac{1}{4!}) (3x)^4-......$ or, $=\cos (3x)$