삼각함수 합성 최대최소

$\displaystyle y = \cos x + 2 ( \sin x \cos \frac{\pi}{6} + \cos x \sin \frac{\pi}{6} )$ $\displaystyle = \cos x + 2 ( \frac{\sqrt{3}}{2} \sin x + \frac{1}{2} \cos x )$ $\displaystyle = \sqrt{3} \sin x + 2 \cos x$ $\displaystyle = \sqrt{7} \sin ( x + \theta ) \left( \sin \theta = \frac{2}{\sqrt{7}} , \cos \theta = \frac{\sqrt{3}}{\sqrt{7}} \right)$ 따라서, $\displaystyle M - m = \sqrt{7} - ( - \sqrt{7} ) = 2 \sqrt{7}$