Question

Evaluate: $\frac{5{\sin }^2{30}^0+{\cos }^2{45}^0+4{\tan }^2{60}^0}{2\sin {30}^0\cos {60}^0+\tan {45}^0}=\frac{55}{m}$.Find $m$

Answer 1

Given, $\frac{5{\sin }^{2}30°+{\cos }^{2}45°+4{\tan }^{2}60°}{2\sin 30°.\cos 60°+\tan 45°}=\frac{55}{m}$

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

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

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