Question

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

• A. $2\frac{5}{16}$
• B. $\frac{67}{12}$
• C. 0
• D. 1

Answer 1

Answer: (B)

$\frac{67}{12}$

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

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

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

= $\frac{15+64-12}{12}$

= $\frac{67}{12}$