Question

What is the value of $\frac{\sin ({30}^{\circ }-A)}{\cos A-\sqrt{3}\sin A}$ ?

Answer 1

$\sin ({30}^0-A)=\sin {30}^0\cos A-\sin A\cos {30}^0$
$=\frac{1}{2}\times \cos A-\sin A\times \frac{\sqrt{3}}{2}$
$=\frac{1}{2}(\cos A-\sqrt{3}\sin A)$
$\therefore \frac{\sin ({30}^0-A)}{\cos A-\sqrt{3}\sin A}=\frac{1}{2}\times \frac{\cos A-\sqrt{3}\sin A}{\cos A-\sqrt{3}\sin A}=\frac{1}{2}$