Question

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

• A. 1
• B. $9\frac{1}{6}$
• C. $7\frac{3}{7}$
• D. $\frac{47}{12}$

Answer 1

The correct option is B $9\frac{1}{6}$

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

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

= $\frac{\frac{5}{4}+\frac{1}{2}+12}{\frac{1}{2}+1}$

= $\frac{\frac{5+48+2}{4}}{\frac{3}{2}}$

= $\frac{55}{6}$

= $9\frac{1}{6}$