Prove that: `(sin5A-sin3A)/(cos5A+cos3A)=tanA` `(sinA-sin3A)/(cosA+cos3A)=tanA`

Explanation

To prove the equations \(\frac{\sin 5A - \sin 3A}{\cos 5A + \cos 3A} = \tan A\) and \(\frac{\sin A - \sin 3A}{\cos A + \cos 3A} = \tan A\), we will use trigonometric identities.

### Proof of the first equation:

1. **Start with the left-hand side (LHS):**
\[ \frac{\sin 5A - \sin 3A}{\cos 5A + \cos 3A} \]
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