Express $\sqrt{3}\sin\theta - \cos\theta$ as: $a\cos (\theta + \alpha) $ Express $\sqrt{3}\sin\theta - \cos\theta$ as: $a\cos (\theta + \alpha) $
Can someone please explain to me how to go about doing this? 

you can write $$\sqrt 3 \sin t - \cos t = 2\left(\frac{\sqrt 3}2 \sin t - \frac 12 \cos t\right) = 2\left(\sin t\sin \left(\frac{\pi}3 \right) - \cos\left(\frac {\pi} 3\right) \cos t\right)= -2\cos \left(t + \frac{\pi}3\right) = 2 \cos \left(t - \frac{2\pi}3\right) $$
