Question

Solve $\frac{\cos {45}^0}{\sec {30}^0+{\text{cosec30}}^0}$

• A. $\frac{3\sqrt{2}-\sqrt{6}}{8}$
• B. $\frac{3-\sqrt{6}}{8}$
• C. $\frac{\sqrt{6}-\sqrt{2}}{2}$
• D. $\frac{3\sqrt{2}-6}{4}$

Answer 1

The correct option is A $\frac{3\sqrt{2}-\sqrt{6}}{8}$

$\left(\frac{cos{45}^{\circ }}{sec{30}^{\circ }+cosec{30}^{\circ }}\right)=\left(\frac{\left(\frac{1}{\sqrt{2}}\right)}{(\frac{2}{\sqrt{3}}+(\frac{2}{1}\left)\right)}\right)\left(\frac{1}{\sqrt{2}}\right)\times \left(\frac{\sqrt{3}}{2(1+\sqrt{3})}\right)\times \left(\frac{\sqrt{3}-1}{\sqrt{3}-1}\right)\left)\right(\frac{3-\sqrt{3}}{4\sqrt{2}})\times (\frac{\sqrt{2}}{\sqrt{2}})=(\frac{3\sqrt{2}-\sqrt{6}}{8})$