P = I u = i^{2} R = i_{m}^{2} R \sin^{2} ω t = \frac{I_{m}^{2} R}{2} (1 - \cos (2 ω t))

${P = Iu = i^2 R = i^2_m R \sin^2 \omega t = \frac {I^2_m R} {2} (1 - \cos(2\omega t))}$