Question

The value of the expression $[\frac{{\sin }^2{22}^o+{\sin }^2{68}^o}{{\cos }^2{22}^o+{\cos }^2{68}^o}+{\sin }^2{63}^o+{\cos }^2{63}^o]$ is

• A. $3$
• B. $2$
• C. $1$
• D. $0$

Answer 1

The correct option is B $2$

$[\frac{{\sin }^2{22}^{\circ }+{\sin }^2{68}^{\circ }}{{\cos }^2{22}^{\circ }+{\cos }^2{68}^{\circ }}+{\sin }^2{63}^{\circ }+{\cos }^2{63}^{\circ }]$

$=[\frac{{\sin }^2{22}^{\circ }+{\sin }^2({90}^{\circ }-{22}^{\circ })}{{\cos }^2{22}^{\circ }+{\cos }^2({90}^{\circ }-{22}^{\circ })}+{\sin }^2{63}^{\circ }+{\cos }^2{63}^{\circ }]$

$=[\frac{{\sin }^2{22}^{\circ }+{\cos }^2{22}^{\circ }}{{\cos }^2{22}^{\circ }+{\sin }^2{22}^{\circ }}+{\sin }^2{63}^{\circ }+{\cos }^2{63}^{\circ }]$

$=\frac{1}{1}+1=2$