Question

If sin α = $\frac{1}{2}$ and cos β = $\frac{1}{2}$, then (α + β) = ?
(a) 0°
(b) 30°
(c) 60°
(d) 90°

Answer 1

(d) 90^o

$$\begin{gathered} \sin \alpha =\frac{1}{2}=\sin {30}^{\mathrm{o}} \\ \Rightarrow \alpha ={30}^{\mathrm{o}} \\ \cos \beta =\frac{1}{2}=\cos {60}^{\mathrm{o}} \\ \Rightarrow \beta ={60}^{\mathrm{o}} \\ \therefore \alpha +\beta ={30}^{\mathrm{o}}+{60}^{\mathrm{o}}={90}^{\mathrm{o}} \end{gathered}$$