# Prove the following

Question:

If $\cos (\alpha+\beta)=\frac{3}{5}, \sin (\alpha-\beta)=\frac{5}{13}$ and $0<\alpha, \beta<\frac{\pi}{4}$, then $\tan (2 \alpha)$ is equal to :

1. $\frac{21}{16}$

2. $\frac{63}{52}$

3. $\frac{33}{52}$

4. $\frac{63}{16}$

Correct Option: , 4

Solution: