Question

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

• A. 0
  
• B. 1
• C. $\sqrt{2}$
• D. $\sqrt{3}$

Answer 1

Answer: (B)

1

$\frac{{\sin }^2{63}^{\circ }+{\sin }^2{27}^{\circ }}{{\cos }^2{17}^{\circ }+{\cos }^2{73}^{\circ }}$
$=\frac{{\left\{\sin \right({90}^{\circ }-{27}^{\circ }\left)\right\}}^2+{\sin }^2{27}^{\circ }}{{\cos }^2{17}^{\circ }+{\left\{\cos \right({90}^{\circ }-{17}^{\circ }\left)\right\}}^2}$
$=\frac{{\cos }^2{27}^{\circ }+{\sin }^2{27}^{\circ }}{{\cos }^2{17}^{\circ }+{\sin }^2{17}^{\circ }}=\frac{1}{1}=1$