Question

Evaluate :
$\frac{3{\tan }^2{30}^{\circ }+{\tan }^2{60}^{\circ }+\text{cosec}{30}^{\circ }-\tan {45}^{\circ }}{{\cot }^2{45}^{\circ }}$

Answer 1

Given that $\frac{3{\tan }^2{30}^{\circ }+{\tan }^2{60}^{\circ }+\text{cosec}{30}^{\circ }-\tan {45}^{\circ }}{{\cot }^2{45}^{\circ }}$

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

$=1+3+2-1$

$=5$