(a) $\sin (\alpha – \beta ) = \frac{1}{2} = \sin 30^\circ \Rightarrow \alpha – \beta = 30^\circ $…..$(i)$

and $\cos (\alpha + \beta ) = \frac{1}{2} \Rightarrow \alpha + \beta = 60^\circ $…..$(ii)$

Solving $(i)$ and $(ii)$, we get $\alpha = 45^\circ $ and $\beta = 15^\circ $.

Trick : In such type of problems, students should satisfy the given conditions with the values given in the options.

Here $\alpha = 45^\circ $ and $\beta = 15^\circ $ satisfy both the conditions.