Question

Express $\sqrt{3}\cos \theta -\sin \theta$ as a single trigonometric ratio

Answer 1

$\sqrt{3}\cos \theta -\sin \theta =2(\frac{\sqrt{3}}{2}\cos \theta -\frac{1}{2}\sin \theta )$
$=2(\cos \theta \cdot \cos {30}^{\circ }-\sin \theta \cdot \sin {30}^{\circ })=2\left(\cos (\theta +{30}^{\circ })\right)$
$\Rightarrow \sqrt{3}\cos \theta -\sin \theta =2\cos (\theta +{30}^{\circ })$