Question

Is there a difference between y=cos^-1(x) and y=(cos x)^-1?

Answer 1

`\cos^(-1)x` could be used to denote the inverse cosine function, while
`(\cos x)^(-1)` probably instead refers to the reciprocal cosine function, i.e. the secant function.

In general,
`\cos^(-1)x\\eq(\cos x)^(-1)`, but it's not unheard of for them to mean the same thing, especially in a context where something like
`\arccos x` is used explicitly to denote the inverse function. I'd be careful about assuming they are always the same.