Why is reduction formula of $\int \cos^n (x) dx$ restricted to n>1?

Question

$$\int\cos^n x \ dx = \frac{1}n \cos^{n-1}x \sin x + \frac{n-1}{n}\int\cos^{n-2} x \ dx$$

is valid for n>1

The derivation of the reduction formula is well-discussed on the forum e.g, but I can't find anywhere explaining why it is only valid for n>1. Can someone explain?