Question

Evaluate: $\frac{5{\sin }^2{30}^0+{\cos }^2{45}^0+4{\tan }^2{60}^0}{2\sin {30}^0\cos {60}^0+\tan {45}^0}$

Answer 1

We have,

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

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

$\Rightarrow \frac{\frac{5}{4}+\frac{1}{2}+4\left(3\right)}{\frac{1}{2}+1}$

$\Rightarrow \frac{\frac{5}{4}+\frac{1}{2}+12}{\frac{3}{2}}$

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

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

$\Rightarrow \frac{55}{6}$

Hence, this is the answer.