Assertion (A): If $\mathrm{z}=\mathrm{i} \log \left(2-\sqrt{3}\right)$ then $\cos \mathrm{z}=2$

Reason (R) : $\cos \mathrm{h} \mathrm{\theta }=\frac{{\mathrm{e}}^{\mathrm{i\theta }}+{\mathrm{e}}^{\mathrm{i\theta }}}{2}$

$$\begin{gathered} \mathbf{Assertion} \\ \mathrm{z}=\mathrm{i} \log (2-\sqrt{3}) \\ \Rightarrow \mathrm{iz}=-\log (2-\sqrt{3})=\log (2+\sqrt{3})\Rightarrow {\mathrm{e}}^{\mathrm{iz}}=2+\sqrt{3} \\ -\mathrm{iz}=\log (2-\sqrt{3})\Rightarrow {\mathrm{e}}^{-\mathrm{iz}}=2-\sqrt{3} \\ \Rightarrow {\mathrm{e}}^{\mathrm{iz}}=\cos \mathrm{z}+\mathrm{i} \sin \mathrm{z}=2+\sqrt{3} \\ \mathrm{and} {\mathrm{e}}^{-\mathrm{iz}}=\cos \mathrm{z}-\mathrm{i} \sin \mathrm{z}=2-\sqrt{3} \\ \therefore 2\cos \mathrm{z}=2+\sqrt{3} + 2-\sqrt{3} \\ \Rightarrow \boxed{\cos \mathrm{z}=2,} \\ \mathbf{Reason}\mathbf{.} \\ \mathrm{cosh\theta }=\frac{{\mathrm{e}}^{\mathrm{\theta }}+{\mathrm{e}}^{-\mathrm{\theta }}}{2} \end{gathered}$$

$\therefore$ I is true,  II is false.