An alternating current is given by the equation i=i1 sinωt+i2 cosωt . The rms current will be:
12i1+i22
12i1+i2
12i12+i2212
Given :i=i1sinωt+i2cosωt⇒i2=i12sin2ωt+i22cos2ωt+2i1i2sinωtcosωt⇒<i2>=i1212+i2212+0 Thus, irms=<i2>=i12+i22212