Question

Express the following as a single trigonometric ratio :

$\sqrt{3}\cos \theta -\sin \theta$

Answer 1

$\sqrt{3}\cos \theta -\sin \theta$

$=2(\frac{\sqrt{3}}{2}\cos \theta -\frac{1}{2}\sin \theta )$

$=2(\cos \theta .\cos {30}^o-\sin \theta .\sin {30}^o)$

$=2\cos (\theta +{30}^o)$