第13章 13.5

(1)

$\cos x - \sin x = \sqrt{2}\left(\frac{1}{\sqrt{2}}\cos x - \frac{1}{\sqrt{2}}\sin x\right) = \sqrt{2}\cos\left(x + \frac{\pi}{4}\right)$

(2)

$\sqrt{3}\sin x - \cos x = 2\left(\frac{\sqrt{3}}{2}\sin x - \frac{1}{2}\cos x\right) = 2\sin\left(x - \frac{\pi}{6}\right)$

(3)

$\sqrt{3}\cos x - \sin x = 2\left(\frac{\sqrt{3}}{2}\cos x - \frac{1}{2}\sin x\right) = 2\cos\left(x + \frac{\pi}{6}\right)$

(4)

$\sqrt{3}\cos x + \sin x = 2\left(\frac{\sqrt{3}}{2}\cos x + \frac{1}{2}\sin x\right) = 2\sin\left(x + \frac{\pi}{3}\right)$