Question

Evaluate :
$\frac{(3ta{n}^2{30}^{\circ }+ta{n}^2{60}^{\circ })+cosec{30}^{\circ }-tan{45}^{\circ }}{co{t}^2{45}^{\circ }}$

Answer 1

$\frac{(3{\tan }^2{30}^{\circ }+{\tan }^2{60}^{\circ })+\text{cosec}{30}^{\circ }-\tan {45}^{\circ }}{{\cot }^2{45}^{\circ }}=\frac{3(\frac{1}{\sqrt{3}}{)}^2+(\sqrt{3}{)}^2+2-1}{(1{)}^2}$

$=\frac{3\times \frac{1}{3}+3+2-1}{1}$

$=\frac{1+3+2-1}{1}$

$=5$