삼각함수 합성 최댓값

[출제의도] 삼각함수의 덧셈정리를 이해하기 $\displaystyle y = \frac{\pi}{3} - x$이므로 (준식) $\displaystyle = \sqrt{3} \cos x + 2 \sin \left( \frac{\pi}{3} - x \right)$ $\displaystyle = 2 \sqrt{3} \cos x - \sin x$ $\displaystyle = \sqrt{13} \sin \left( \alpha - x \right)$ $\displaystyle \left( \begin{array}{l} \begin{matrix} \\ \end{matrix} \end{array} \right.$단, $\displaystyle \sin \alpha = \frac{2 \sqrt{39}}{13}$, $\displaystyle \cos \alpha = \frac{\sqrt{13}}{13}$$\displaystyle \begin{matrix} \\ \end{matrix} )$ 따라서 최댓값은 $\displaystyle \sqrt{13}$