Question

What is the value of $\frac{{\sin }^2{30}^0}{{\cos }^2{30}^0}+\frac{{\cos }^2{30}^0}{{\sin }^2{30}^0}$ ?

Answer 1

The given expression is equal to
$=\frac{{\left(\frac{1}{2}\right)}^2}{{\left(\frac{\sqrt{3}}{2}\right)}^2}+\frac{{\left(\frac{\sqrt{3}}{2}\right)}^2}{{\left(\frac{1}{2}\right)}^2}=\frac{\frac{1}{4}}{\frac{3}{4}}+\frac{\frac{3}{4}}{\frac{1}{4}}+3=3\frac{1}{3}$