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:

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