Question

Question 10
If $sin\alpha =\frac{1}{2}$ and $cos\beta =\frac{1}{2}$, then the value of $(\alpha +\beta )$ is

(A) $0^{\circ }$
(B) ${30}^{\circ }$
(C) ${60}^{\circ }$
(D) ${90}^{\circ }$

Answer 1

The answer is (D).

Given, $Given,sin\alpha =\frac{1}{2}=sin{30}^{\circ }[\because sin{30}^{\circ }=\frac{1}{2}]$

$\Rightarrow \alpha ={30}^{\circ }$

And $cos\beta =\frac{1}{2}=cos{60}^{\circ }[\because cos{60}^{\circ }=\frac{1}{2}]$

$\Rightarrow \beta ={60}^{\circ }$

$\therefore \alpha +\beta ={30}^{\circ }+{60}^{\circ }={90}^{\circ }$