Question

Evaluate $\frac{\cos {45}^0}{\sec {30}^0+\text{cosec}{30}^0}$

• A. $\frac{\sqrt{2}}{\sqrt{3}+1}$
• B. $\frac{\sqrt{3}}{2\sqrt{2}+2\sqrt{6}}$
• C. $\frac{\sqrt{2}}{\sqrt{2}+1}$
  
• D. $\frac{\sqrt{2}}{\sqrt{3}+2}$
  

Answer 1

Answer: (B)

$\frac{\sqrt{3}}{2\sqrt{2}+2\sqrt{6}}$

$\frac{\cos 45°}{\sec 30°+\text{cosec}30°}$

$\frac{\cos 45°}{\frac{1}{\cos 30°}+\frac{1}{\sin 30°}}=\frac{\frac{1}{\sqrt{2}}}{\frac{1}{\frac{\sqrt{3}}{2}}+\frac{1}{\frac{1}{2}}}$

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

$=\frac{\sqrt{3}}{\sqrt{2}(2+2\sqrt{3})}$

$=\frac{\sqrt{3}}{2\sqrt{2}+2\sqrt{6}}$