Question

Find the value of
$\frac{1+sin{30}^{\circ }}{cos{30}^{\circ }}+\frac{cos{30}^{\circ }}{1+sin{30}^{\circ }}.$

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

Answer 1

The correct option is A

$\frac{4}{\sqrt{3}}$

$\frac{1+sin{30}^{\circ }}{cos{30}^{\circ }}+\frac{cos{30}^{\circ }}{1+sin{30}^{\circ }}$

$=\frac{1+\frac{1}{2}}{\frac{\sqrt{3}}{2}}+\frac{\frac{\sqrt{3}}{2}}{1+\frac{1}{2}}$

$=\frac{3}{\sqrt{3}}+\frac{\sqrt{3}}{3}$

$=\sqrt{3}+\frac{1}{\sqrt{3}}$

$=\frac{3+1}{\sqrt{3}}$

$=\frac{4}{\sqrt{3}}$