Signal
$ y(t)=2cos(t) $
Energy
We will find the energy in one cycle of the cosine waveform.
$ E=\int_0^{2\pi}{|2cos(t)|^2dt} $
$ =\int_0^{2\pi}{(2(2cos(t)^2-1)+2)dt} $
$ =\int_0^{2\pi}{2+cos(2t))dt $
$ =(2t+sin(2t))|_{t=0}^{t=2\pi} $
$ =(4\pi+0-0-0) $
$ =4\pi $