question_answer

\[Cos(A+B)=\frac{1}{2}\]and\[sin(A-B)=\frac{1}{2},\,\,{{0}^{o}}<A+B<{{90}^{o}}\]and\[A-B>{{0}^{o}}\], find the values of \[\angle A\]and\[\angle B\].

A) \[~\angle A={{60}^{o}}\,,\angle B={{30}^{o}}\]       

B) \[\angle A={{15}^{o}},\text{ }\angle B={{45}^{o}}\]

C) \[\angle A={{30}^{o}},\,\,\angle B={{15}^{o}}\]

D) \[\angle A=45{}^\circ ,\text{ }\angle B=15{}^\circ \]

E) None of these