Question

The value of $\frac{\sqrt{3}}{\sin {15}^o}-\frac{1}{\cos {15}^o}$ is equal to

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

Answer 1

Answer: (A)

$4\sqrt{2}$

$\frac{\sqrt{3}}{\sin {15}^o}-\frac{1}{\cos {15}^o}$
$=\frac{\sqrt{3}\cos {15}^o-\sin {15}^o}{\sin {15}^o\cos {15}^o}$
$=\frac{\sin {60}^o\cos {15}^o-\cos {60}^o\sin {60}^o}{\frac{1}{4}\left(\sin {30}^o\right)}$
$=\frac{\sin ({60}^o-{15}^o)}{\frac{1}{4}\times \frac{1}{2}}$
$=8\times \frac{1}{\sqrt{2}}=4\sqrt{2}$