Assertion(A): The maximum value of$2{\cos }^2\theta +\sqrt{5}\cos \theta \sin \theta +4{\sin }^2\theta \text{ is }\frac{9}{2}$

Reason (R): The maximum value of $a{\cos }^2\theta +b\cos \theta \sin \theta +c{\sin }^2\theta \mathrm{is} \frac{1}{2}\left[(\mathrm{a}+\mathrm{c})+\sqrt{(\mathrm{a}-\mathrm{c}{)}^2+{\mathrm{b}}^2}\right]$

$$\begin{gathered} a{\cos }^2\theta +b\cos \theta \sin \theta +c{\sin }^2\theta =\frac{1}{2}\left(a(2{\cos }^2\theta +b(2\sin \theta \cos \theta )+c(2{\sin }^2\theta )\right) \\ =\frac{1}{2}\left(a(1+\cos 2\theta )+bSin2\theta +c(1-\cos 2\theta )\right) \\ =\frac{1}{2}\left((a+c)+(a-c)\cos 2\theta +b\sin 2\theta \right) \\ Maximum Value =\frac{1}{2}\left(\left(a+c\right)+\sqrt{{\left(a-c\right)}^2+b^2}\right) \\ substitute \\ a=2,c=4,b=\sqrt{5} \\ The maximum value of 2{\cos }^2\theta +\sqrt{5}\cos \theta \sin \theta +4{\sin }^2\theta \text{ is }\frac{9}{2} \end{gathered}$$