question_answer

Let \[\cos \,(\alpha +\beta )=\frac{4}{5}\] and let \[sin\,(\alpha -\beta )=\frac{5}{13},\] where \[0\le \alpha ,\beta \le \frac{\pi }{4}\].Then tan \[2\alpha \] is equal to

A)  \[\frac{25}{16}\]                                  

B)  \[\frac{56}{33}\]

C)  \[\frac{19}{12}\]                                  

D)  \[\frac{20}{7}\]

E)  None of these