Question

Evaluate:$\frac{{\sin }^2{63}^0+{\sin }^2{27}^o}{{\cos }^2{17}^o+{\cos }^2{73}^o}$.

Answer 1

Now,

Let $a=\frac{{\sin }^2{63}^0+{\sin }^2{27}^o}{{\cos }^2{17}^o+{\cos }^2{73}^o}$

$=\frac{{\sin }^2({90}^o-{27}^o)+{\sin }^2{27}^o}{{\cos }^2({90}^o-{73}^o)+{\cos }^2{73}^o}$

$=\frac{{\cos }^2\left({27}^o\right)+{\sin }^2{27}^o}{{\sin }^2\left({73}^o\right)+{\cos }^2{73}^o}$

We know that, ${\sin }^{2}x+{\cos }^{2}x=1$

$a=\frac{1}{1}$

$a=1$.