Question

The value of the expression $[\frac{{\sin }^2{22}^0+{\sin }^2{68}^0}{{\cos }^2{22}^0+{\cos }^2{68}^0}+{\sin }^2{63}^0+\cos {63}^0\sin {27}^0]$ is

• A. $3$
• B. $2$
• C. $1$
• D. $0$

Answer 1

The correct option is B $2$

$(\frac{{\sin }^{2}22+{\sin }^{2}68}{{\cos }^{2}22+{\cos }^{2}68}+{\sin }^{2}63+\cos 63\sin 27)$

$=\{\frac{{\sin }^2\left(90-68\right)+{\sin }^{2}68}{{\cos }^2(90-68)+{\cos }^{2}68}+{\sin }^{2}63+\cos 63\sin \left(90-63\right)\}$

$=\{\frac{{\cos }^{2}68+{\sin }^{2}68}{{\sin }^{2}68+{\cos }^{2}68}+{\sin }^{2}63+\cos 63\cos 63\}$

$=(1+{\sin }^{2}63+{\cos }^{2}63)$

$=1+1$

$=2$