What is the unit-power information signal?
The power of a deterministic signal $s(t)$ is given by
$$P_s=\lim_{T\to\infty}\frac{1}{2T}\int_{-T}^Ts^2(t)dt\tag{1}$$
A unit power signal is obtained by normalizing $s(t)$ by the root of its power:
$$\hat{s}(t)=\frac{s(t)}{\sqrt{P_s}}\tag{2}$$
In the case of $s(t)=A\cos(2\pi f_0t)$ you obtain from $(1)$
$$P_s=\lim_{T\to\infty}\frac{1}{2T}\int_{-T}^TA^2\cos^2(2\pi f_0t)dt=\frac{A^2}{2}\tag{3}$$
So the corresponding unit power signal is
$$\hat{s}(t)=\frac{\sqrt{2}}{A}s(t)=\sqrt{2}\cos(2\pi f_0t)\tag{4}$$