삼각함수 최댓값

$\displaystyle f ( x ) = \sin x + \sqrt{3} \cos x + \sqrt{5} \cos \left( x + \frac{\pi}{3} \right)$ $\displaystyle = 2 \left( \frac{1}{2} \sin x + \frac{\sqrt{3}}{2} \cos x \right) + \sqrt{5} \cos \left( x + \frac{\pi}{3} \right)$ $\displaystyle = 2 \sin \left( x + \frac{\pi}{3} \right) + \sqrt{5} \cos \left( x + \frac{\pi}{3} \right)$ $\displaystyle = 3 \left\{ \frac{2}{3} \sin \left( x + \frac{\pi}{3} \right) + \frac{\sqrt{5}}{3} \cos \left( x + \frac{\pi}{3} \right) \right\}$ $\displaystyle = 3 \sin \left( x + \frac{\pi}{3} + \theta \right)$ (단, $\displaystyle \tan \theta = \frac{\sqrt{5}}{2}$)$= 3$