Question

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

Answer 1

$\frac{si{n}^2{63}^{\circ }+si{n}^2{27}^{\circ }}{co{s}^2{17}^{\circ }+co{s}^2{73}^{\circ }}=\frac{si{n}^2(90-27{)}^{\circ }+si{n}^2{27}^{\circ }}{co{s}^2(90-73{)}^{\circ }+co{s}^2{73}^{\circ }}=\frac{1}{1}=1$

$[\because cos(90-\theta )=sin\theta$ and $sin(90-\theta )=cos\theta ]$