While arccosine and cosine do cancel out, there's still the problem of domain. Arccos(x) itself is only defined within that domain of [-1,1]. That means you can't plug in anything less than -1 or greater than 1 and get an answer out. Cos(arccos(x)) is a composite function.

What is arccos to COS?

Arccos definition

The arccosine of x is defined as the inverse cosine function of x when -1≤x≤1. (Here cos^-1 x means the inverse cosine and does not mean cosine to the power of -1).

What is the difference between arccos and cos?

is that arccosine is (trigonometry) any of several single-valued or multivalued functions that are inverses of the cosine function symbol: arccos, cos^-1 while cosine is (trigonometry) in a right triangle, the ratio of the length of the side adjacent to an acute angle to the length of the hypotenuse symbol: cos.