Question

Evaluate:
$\frac{{\cos }^2{40}^o+{\cos }^2{50}^o}{{\sin }^2{40}^o+{\sin }^2{50}^o}$

Answer 1

We have,

$\Rightarrow \frac{{\cos }^2{40}^0+{\cos }^2{50}^0}{{\sin }^2{40}^0+{\sin }^2{50}^0}$

$\Rightarrow \frac{{\cos }^2({90}^0-{50}^0)+{\cos }^2{50}^0}{{\sin }^2({90}^0-{50}^0)+{\sin }^2{50}^0}$

$\Rightarrow \frac{{\sin }^2{50}^0+{\cos }^2{50}^0}{{\cos }^2{50}^0+{\sin }^2{50}^0}$

$\Rightarrow \frac{1}{1}$

$\Rightarrow 1$

Hence, this is the answer.