Question

rms value of i= 10 sinwt + 20 cos (wt + 30°)

Answer 1

The rms value by definition

$$i_{\rm rms}=\sqrt{\frac{1}{T}\int_{0}^{T}i^2(t)dt}$$

$$\int_{0}^{T}(10\sin (2\pi t/T) + 20\cos (2\pi t/T + 30°))^2dt$$

$$=150T$$

Finally

$$i_{\rm rms}=\sqrt{150}=12.2$$