Question

Simplify $\frac{5{\cos }^2{60}^0+4{\sec }^2{30}^0-{\tan }^2{45}^0}{{\sin }^2{30}^0+{\cos }^2{30}^0}$

• A. $-\frac{55}{2}$
• B. $\frac{67}{12}$
• C. $\frac{5}{12}$
• D. $\frac{55}{4}$

Answer 1

The correct option is B $\frac{67}{12}$

$\frac{5{\cos }^{2}60°+4{\sec }^{2}30°-{\tan }^{2}45°}{{\sin }^{2}30°+{\cos }^{2}30°}$

$=\frac{5{\left(\frac{1}{2}\right)}^2+4({\frac{2}{\sqrt{3}})}^2-1}{1}$

$=\frac{5}{4}+\frac{16}{3}-1$

$=\frac{67}{12}$