Mathematics

Problem

Let

\cos(\alpha + \beta) = \frac{4}{5}

and

\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}

\frac{56}{33}

\frac{19}{12}

\frac{20}{7}