Question

If $\alpha +\beta ={90}^{\circ }$ and $\alpha =2\beta$, then ${\cos }^2\alpha +{\sin }^2\beta$ equals to

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

Answer 1

Answer: (A)

$\frac{1}{2}$

$\alpha +\beta ={90}^{\circ }$ and $\alpha =2\beta$
$\therefore \alpha ={60}^{\circ }$ and $\beta ={30}^{\circ }$
$\therefore {\cos }^2\alpha +{\sin }^2\beta ={\cos }^2{60}^{\circ }+{\sin }^2{30}^{\circ }$
$=\frac{1}{4}+\frac{1}{4}=\frac{1}{2}$