x+ 3 x is maximum when x is equal to

Given expression is $f(x) = \cos x + \sqrt{3} \sin x$

Multiplying and dividing by $\sqrt{1^2 + (\sqrt{3})^2} = 2$

$f(x) = 2 \left( \dfrac{1}{2} \cosx + \dfrac{\sqrt{3}}{2} \sinx \right)<br><br>$f(x) = 2 \left( \cos \dfrac{\pi}{3} \cos$x + \sin$\dfrac{\pi}{3} \sinx \right)

f(x) = 2 \cos \left(x - \dfrac{\pi}{3} \right)<br><br>The maximum value of\cos \left( x - \dfrac{\pi}{3} \right)$is$1$, which occurs when$x - \dfrac{\pi}{3} = 0$<br><br>$x = \dfrac{\pi}{3}$<br><br>Answer:$\dfrac{\pi}{3}