Prove that: `(sin5A-sin3A)/(cos5A+cos3A)=t a n A`

Explanation

To prove that \(\frac{\sin 5A - \sin 3A}{\cos 5A + \cos 3A} = \tan A\), we will use the transformation formulas for sine and cosine.

### Step 1: Apply the sine difference formula
We know that:
\[ \sin x - \sin y = 2 \cos\left(\frac{x+y}{2}\right) \sin\left(\frac{x-y}{2}\right) \]
Let \(x = 5A\) and \(y = 3A\). Then:
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