<prompt> Expand this cosine functioncos x  <response>: The cosine function, cosx, can be expanded into its Taylor series representation as:cosx 1 - x22! x44! - x66! ... -1nx2n2n!where n is a non-negative integer and ! denotes the factorial function.The series representation of cosx around 0 is an alternating series of even-powered polynomial terms with corresponding coefficients being the reciprocal of the factorial of the power:cosx sum-1n x2n 2n!, for n 0 to infinity.This expansion can be used to approximate the value of the cosine function for any value of x, with more terms in the expansion resulting in a more accurate approximation. 