Question

Evaluate the following.
$\frac{{\sec }^2{60}^o-{\tan }^2{60}^o}{{\sin }^2{30}^o+{\cos }^2{30}^o}$

Answer 1

$\frac{{\sec }^2{45}^o-{\tan }^2{60}^o}{{\sin }^2{30}^o-{\cos }^{2}45}=\frac{(\sqrt{2}{)}^2-(\sqrt{3}{)}^2}{{\left(\frac{1}{2}\right)}^2-{\left(\frac{1}{\sqrt{2}}\right)}^2}$

$\Rightarrow \frac{2-3}{\frac{1}{4}-\frac{1}{2}}=\frac{-1}{-1/4}=4$.