Question

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

• A. $4$
• B. $3$
• C. $-3$
• D. $-1$

Answer 1

The correct option is A $4$

Given expression is $\frac{1}{sin{10}^{\circ }}-\frac{\sqrt{3}}{cos{10}^{\circ }}$

$=2(\frac{1/2}{sin{10}^{\circ }}-\frac{\sqrt{3}/2}{cos{10}^{\circ }})$

$=2(\frac{cos{60}^{\circ }}{sin{10}^{\circ }}-\frac{sin{60}^{\circ }}{cos{10}^{\circ }})$

$=2\left(\frac{cos{60}^{\circ }cos{10}^{\circ }-sin{60}^{\circ }sin{10}^{\circ }}{sin{10}^{\circ }cos{10}^{\circ }}\right)$

$=2\left(\frac{cos({60}^{\circ }+{10}^{\circ })}{sin{10}^{\circ }cos{10}^{\circ }}\right)$

$=2\frac{\cos 70}{\sin 10\cos 10}$

$=4\frac{\cos 70}{sin20}$

$=4\frac{sin20}{sin20}$

$=4$