Question

Find the value of:
${\csc }^2{60}^o-{\tan }^2{30}^o$

Answer 1

${\csc }^2{60}^{\circ }-{\tan }^2{30}^{\circ }$

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

$=\frac{4}{3}-\frac{1}{3}$

$=\frac{4-1}{3}$

$=\frac{3}{3}=1$