The RMS value of emf given by E = ( 8 sin ω t + 6 cos ω t ) volt is

The given function is,

$$\begin{gathered} E=2\left(4\sin \omega t+3\cos \omega t\right)=\frac{2\times 5}{1}\left(\frac{4}{5}\sin \omega t+\frac{3}{5}\cos \omega t\right) \\ =10\left(\cos \theta \sin \omega t+\sin \theta \cos \omega t\right)=10\sin \left(\omega t+\theta \right) \\ E=10\sin \left(\omega t+\theta \right) \end{gathered}$$

compare it with,

$E=E_0\sin \left(\omega t+\theta \right)$

so $E_0=10 \mathrm{V} \& E_{\mathrm{RMS}}=\frac{{\mathit{E}}_{\mathit{0}}}{\sqrt{\mathit{2}}}=\frac{10 \mathrm{V} }{\sqrt{2}}=5\sqrt{2} \mathrm{V}$