Question

What is the value of
${\left(\frac{\sin {77}^o}{\cos {13}^o}\right)}^2+{\left(\frac{\cos {77}^o}{\sin {13}^o}\right)}^2-2{\cos }^2{45}^o$

Answer 1

$(\frac{\sin {77}^o}{\cos {13}^o}{)}^2+(\frac{\cos {77}^o}{\sin {13}^o}{)}^2-2(\frac{1}{\sqrt{2}}{)}^2=(\frac{\sin {77}^o}{\sin {77}^o}{)}^2+(\frac{\cos {77}^o}{\cos {77}^o}{)}^2-1$

$=1+1-1=1$