Question

The value of $\sqrt{3}\text{cosec}{20}^0-\sec {20}^0$ is

• A. $4.5$
• B. $4$
• C. $8$
• D. $9$

Answer 1

The correct option is B $4$

The value of $\sqrt{3}\csc {20}^{\circ }-\sec {20}^{\circ }$ is

$2\left(\frac{\sqrt{3}}{2}\csc {20}^{\circ }-\frac{1}{2}\sec {20}^{\circ }\right)$

$=2\left(\sin {60}^{\circ }.\csc {20}^{\circ }-\cos {60}^{\circ }.\sec {20}^{\circ }\right)$

$=2(\frac{\sin {60}^{\circ }}{\sin {20}^{\circ }}-\frac{\cos {60}^{\circ }}{\cos {20}^{\circ }})$

$=2\left(\frac{\sin {60}^{\circ }.\cos {20}^{\circ }-\sin {20}^{\circ }.\cos {60}^{\circ }}{\sin {20}^{\circ }.\cos {20}^{\circ }}\right)$

$=2\frac{\sin ({60}^{\circ }-{20}^{\circ })}{\sin {20}^{\circ }.\cos {20}^{\circ }}$

$=\frac{2\sin 2\left({20}^{\circ }\right)}{\sin {20}^{\circ }.\cos {20}^{\circ }}$

$=\frac{4\sin {20}^{\circ }.\cos {20}^{\circ }}{\sin {20}^{\circ }.\cos {20}^{\circ }}=4$