If `cos(alpha+beta)=3/5, sin(alpha-beta)=5/13`, and `0 lt alpha, beta lt pi/4`, then `tan(2alpha)` is equal to:

Options

A. `21/16`
B. `63/52`
C. `33/52`
D. `63/16`

Explanation

To solve the problem, we need to find the value of \( \tan(2\alpha) \) given that \( \cos(\alpha + \beta) = \frac{3}{5} \) and \( \sin(\alpha - \beta) = \frac{5}{13} \).

### Step 1: Find \( \sin(\alpha + \beta) \)

Using the Pythagorean identity, we know that:

\[
\sin^2(\theta) + \cos^2(\theta) = 1
...