A) \[\alpha =45{}^\circ ,\beta =15{}^\circ \]
B) \[\alpha =15{}^\circ ,\beta =45{}^\circ \]
C) \[\alpha =60{}^\circ ,\beta =15{}^\circ \]
D) None of these
Correct Answer: A
Solution :
\[\sin (\alpha -\beta )=\frac{1}{2}=\sin 30{}^\circ \Rightarrow \alpha -\beta =30{}^\circ \] ?..(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.
You need to login to perform this action.
You will be redirected in
3 sec
