The magnitude of resultant vector $R^{\prime}=\sqrt{a^2+b^2+2 a b \cos \theta}$ Here $\mathrm{a}=\mathrm{b}=\mathrm{R}$ Then $R^{\prime}=\sqrt{R^2+R^2+2 R^2 \cos \theta}$ $$ \begin{aligned} & =R \sqrt{2} \sqrt{1+\cos \theta} \\ & =\sqrt{2} R \sqrt{2 \cos ^2 \frac{\theta}{2}} \\ & =2 R \cos \frac{\theta}{2} \end{aligned} $$