Question

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

• A. $0$
• B. $1$
• C. $2$
• D. $4$

Answer 1

The correct option is D $4$

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

$=\frac{\cos {10}^o-\sqrt{3}\sin {10}^o}{\frac{2}{2}\sin {10}^o\cos {10}^o}$
$=\frac{2\{\frac{1}{2}\cos {10}^o-\frac{\sqrt{3}}{2}\sin {10}^o\}}{\frac{2}{2}\sin {10}^o\cos {10}^o}$

$=\frac{4\sin {20}^o}{\sin {20}^o}$ ........ $[\because \sin a\cos b-\cos a\sin b=\sin (a-b)\text{and}2\sin x\cos x=\sin 2x]$

$=4$