The maximum value of e^{(2 + sqrt{3} cos x + | vedclass

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(C) Let $f(x) = 2 + \sqrt{3} \cos x + \sin x$. To find the maximum value of $e^{f(x)}$,we need to find the maximum value of $f(x)$. We know that the e

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$e^{4}$

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(C) Let $f(x) = 2 + \sqrt{3} \cos x + \sin x$. To find the maximum value of $e^{f(x)}$,we need to find the maximum value of $f(x)$. We know that the expression $a \cos x + b \sin x$ lies in the interval $[-\sqrt{a^2 + b^2}, \sqrt{a^2 + b^2}]$. Here,$a = \sqrt{3}$ and $b = 1$. So,$\sqrt{a^2 + b^2} = \sqrt{(\sqrt{3})^2 + 1^2} = \sqrt{3 + 1} = \sqrt{4} = 2$. Thus,the maximum value of $\sqrt{3} \cos x + \sin x$ is $2$. Therefore,the maximum value of $f(x) = 2 + (\sqrt{3} \cos x + \sin x)$ is $2 + 2 = 4$. Hence,the maximum value of $e^{f(x)}$ is $e^{4}$.

The maximum value of $e^{(2 + \sqrt{3} \cos x + \sin x)}$ is

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