Question

Evaluate ${\cos }^2{60}^{\circ }{\sin }^2{30}^{\circ }+{\tan }^2{30}^{\circ }{\cot }^2{60}^{\circ }$

Answer 1

${\cos }^{2}60°{\sin }^{2}30°+{\tan }^{2}30°{\cot }^{2}60°$

$\Rightarrow {\left(\frac{1}{2}\right)}^2{\left(\frac{1}{2}\right)}^2+{\left(\frac{1}{\sqrt{3}}\right)}^2.{\left(\frac{1}{\sqrt{3}}\right)}^2=\frac{1}{16}+\frac{1}{9}=\frac{9+16}{144}$

$=\frac{25}{144}$

Hence, the answer is $\frac{25}{144}.$