Question

The value of the expression $\frac{5{\sin }^2{30}^{\circ }+{\cos }^2{45}^{\circ }+4{\tan }^2{60}^{\circ }}{2\sin {30}^{\circ }\cos {60}^{\circ }+\tan {45}^{\circ }}$ is

• A. 4
• B. 9
• C. $\frac{53}{12}$
• D. $\frac{55}{6}$

Answer 1

Answer: (D)

$\frac{55}{6}$

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

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

$=\frac{\frac{5}{4}+\frac{1}{2}+4\times 3}{\frac{1}{2}+1}$

$=\frac{\frac{7}{4}+12}{\frac{3}{2}}$

$=\frac{\frac{55}{4}}{\frac{3}{2}}$

$=\frac{55}{6}$

Option D is correct.