Question

Find the value of: $\frac{{\cos }^2{34}^{\circ }+{\cos }^2{56}^{\circ }}{{\sin }^2{59}^{\circ }+{\sin }^2{31}^{\circ }}$

Answer 1

Consider the given expression,

$\Rightarrow \frac{{\cos }^2{34}^0+{\cos }^{2}56}{{\sin }^{2}59+{\sin }^{2}31}$

$\Rightarrow \frac{{\cos }^2{34}^0+{\cos }^2({90}^0-{34}^0)}{{\sin }^{2}59+{\sin }^2({90}^0-{59}^0)}$

$\Rightarrow \frac{{\cos }^2{34}^0+{\sin }^2{34}^0}{{\sin }^{2}59+{\sin }^2{59}^0}$

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

$\Rightarrow 1$