Answer
$\cos (2)=1-\dfrac{2^2}{2!}+\dfrac{2^4}{4!}-\dfrac{2^6}{6!}$
Work Step by Step
The first $4$ non-zero terms of Taylor series can be written as: $\cos x=1-\dfrac{x^2}{2!}+\dfrac{x^4}{4!}-\dfrac{x^6}{6!}$
Plug $x=2$ in the above equation to obtain:
$\cos (2)=1-\dfrac{2^2}{2!}+\dfrac{2^4}{4!}-\dfrac{2^6}{6!}$
Therefore, the first $4$ non-zero terms of an infinite series is equal to:
$\cos (2)=1-\dfrac{2^2}{2!}+\dfrac{2^4}{4!}-\dfrac{2^6}{6!}$
