Prove that : `sin x+sin3x+sin5x+sin7x=4cos x\ cos2xsin4x`

Explanation

To prove that \( \sin x + \sin 3x + \sin 5x + \sin 7x = 4 \cos x \cos 2x \sin 4x \), we will manipulate the left-hand side (LHS) and show that it equals the right-hand side (RHS).

### Step-by-step Solution:

1. **Start with the LHS**:
\[ \text{LHS} = \sin x + \sin 3x + \sin 5x + \sin 7x \]
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