Question

The value of $\frac{1}{\sin {10}^o}-\frac{\sqrt{3}}{\cos {10}^o}$ is:-

• A. $2$
• B. $3$
• C. $4$
• D. $\frac{1}{4}$

Answer 1

The correct option is A $2$

$\frac{1}{\sin {10}^o}-\frac{\sqrt{3}}{\cos {10}^o}$

$4\left[\frac{\frac{1}{2}\cos 10-\frac{\sqrt{3}}{2}\sin 10}{2\sin {10}^o\cos {10}^o}\right]$

$=4\left[\frac{\sin {30}^o\cos {10}^o-\cos 30\sin {10}^o}{2\sin {10}^o\cos {10}^o}\right]$

$=4\left[\frac{\sin 20}{\sin 20}\right]=4$