Prove that:`(sin5x+sin3x)/(cos5x+cos3x)=tan4x`

Explanation

To prove that \(\frac{\sin 5x + \sin 3x}{\cos 5x + \cos 3x} = \tan 4x\), we will start by simplifying the left-hand side (LHS) using trigonometric identities.

### Step 1: Write down the LHS
\[ \text{LHS} = \frac{\sin 5x + \sin 3x}{\cos 5x + \cos 3x} \]

### Step 2: Use the sum-to-product identities
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