Explanation

The Maclaurin series expansion of cos(x) is derived from its Taylor series expansion around x = 0:

cos(x) = 1 - x²/2! + x⁴/4! - x⁶/6! + ...

This series alternates signs and involves even powers of x, with factorials in the denominators.

The answer is cosx = 1 - x²/2! + x⁴/4! - x⁶/6! + ...