An alternating current is given by the equation I = I1 cos(omega t) + I2 sin(omega t). The root mean square (rms) value of this current is:

The given current can be rewritten as a single harmonic oscillation: $I = \sqrt{I_1^2 + I_2^2} \sin(\omega t + \phi)$, where $\tan\phi = \frac{I_1}{I_2}$. The rms value of a sinusoidal current $I_0 \sin(\omega t + \phi)$ is given by $I_{\text{rms}} = \frac{I_0}{\sqrt{2}}$. Here, the peak current $I_0 = \sqrt{I_1^2 + I_2^2}$. Therefore, $I_{\text{rms}} = \sqrt{\frac{I_1^2 + I_2^2}{2}}$.