Question

Find the value of $\frac{1}{\sin {10}^0}-\frac{\sqrt{3}}{\cos {10}^0}$

Answer 1

$\frac{1}{\sin {10}^0}-\frac{\sqrt{3}}{\cos {10}^0}=\frac{\cos {10}^0-\sqrt{3}\sin {10}^0}{\sin {10}^0\cos {10}^0}$
$=2\times (\frac{1}{2}\cos {10}^0-\frac{\sqrt{3}}{2}\sin {10}^0)÷\sin {10}^0\cos {10}^0$
$=2\times (\sin {30}^0\cos {10}^0-\cos {30}^0\sin {10}^0)+\sin {10}^0\cos {10}^0$
$=2\sin ({30}^0-{10}^0)÷\sin {10}^0\cos {10}^0$
$=2\sin {20}^0÷\sin {10}^0\cos {10}^0$
$=\frac{2\times 2\sin {10}^0{\cos }^0}{\sin {10}^0\cos {10}^0}=4$