Question

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

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

Answer 1

The correct option is C $\frac{1}{2}$

$\alpha =2\beta$ and $\alpha +\beta ={90}^{\circ }$

$\therefore \beta ={30}^{\circ }and\alpha ={60}^{\circ }$

$co{s}^2\alpha +si{n}^2\beta =\frac{1}{4}+\frac{1}{4}=\frac{1}{2}$