The average power in AC circuit is given by
Pavg = VI cos φ
where
V = vo sin wt
I = io sin wt
Therefore,
P = vo io sin2 wt cosφ
P = vo io sin2 (2 π f t) cosφ ... as w = 2πf
Now substituting the value of frequency f=n as given,
the relationship changes to
P = vo io sin2 (2 π n t) cosφ