Question

Find the value of $\frac{\text{Cot}{30}^{\circ }+\text{Cosec}{30}^{\circ }}{\text{Cot}{60}^{\circ }-\text{Cosec}{60}^{\circ }}$

• A. $-3-2\sqrt{3}$
• B. $7\sqrt{3}-12$
• C. $9\sqrt{3}+2$
• D. $4\sqrt{3}-2$

Answer 1

The correct option is A $-3-2\sqrt{3}$

Cot ${30}^{\circ }=\sqrt{3},$ cosec ${30}^{\circ }=2$
Cot ${60}^{\circ }=\frac{1}{\sqrt{3}},$ cosec ${60}^{\circ }=\frac{2}{\sqrt{3}}$
Put all the value of standard trigonometric ratio in the given expression,
$\frac{\text{Cot}{30}^{\circ }+\text{Cosec}{30}^{\circ }}{\text{Cot}{60}^{\circ }-\text{Cosec}{60}^{\circ }}=\frac{\sqrt{3}+2}{\frac{1}{\sqrt{3}}-\frac{2}{\sqrt{3}}}$
On simpifying, we get,
$\frac{\text{Cot}{30}^{\circ }+\text{Cosec}{30}^{\circ }}{\text{Cot}{60}^{\circ }-Cosec{60}^{\circ }}=-3-2\sqrt{3}$