삼각함수 합성의 최댓값

$\displaystyle f ( x ) = 2 \cos \left( x - \frac{\pi}{3} \right) + 2 \sqrt{3} \sin x$ $\displaystyle = 2 \left( \cos x \cdot \cos \frac{\pi}{3} + \sin x \cdot \sin \frac{\pi}{3} \right) + 2 \sqrt{3} \sin x$ $\displaystyle = \cos x + \sqrt{3} \sin x + 2 \sqrt{3} \sin x$ $\displaystyle = 3 \sqrt{3} \sin x + \cos x$$\displaystyle = \sqrt{28} \sin ( x + \theta )$ $\displaystyle \left( \text{단} , \sin \theta = \frac{1}{\sqrt{28}} , \cos \theta = \frac{3 \sqrt{3}}{\sqrt{28}} \right)$ 최댓값 $\displaystyle a = \sqrt{28}$ 따라서 $a ^{2} = 28$