Question

Given that $\sin \alpha =\frac{1}{2}$ and $\cos \beta =\frac{1}{2}$, then the value of $(\alpha +\beta )$ is:

• A. $0^0$
• B. ${30}^0$
• C. ${60}^0$
• D. ${90}^0$

Answer 1

The correct option is D ${90}^0$

$\sin \alpha =\frac{1}{2}$

$\because \sin {30}^0=\frac{1}{2}$

$\therefore \alpha ={30}^0$

$\cos \beta =\frac{1}{2}$

$\because \cos {60}^0=\frac{1}{2}$

$\therefore \beta ={60}^0$

Hence, $\alpha +\beta ={30}^0+{60}^0$

$\alpha +\beta ={90}^0$