Find the general solution of `sin5x cos 3x = sin9x cos7x`

Explanation

To find the general solution of the equation \( \sin 5x \cos 3x = \sin 9x \cos 7x \), we can follow these steps:

### Step 1: Apply the double angle identity
We can use the identity \( 2 \sin A \cos B = \sin(A + B) + \sin(A - B) \) to rewrite both sides of the equation:
\[ \sin 5x \cos 3x = \frac{1}{2} \left( \sin(5x + 3x) + \sin(5x - 3x) \right) = \frac{1}{2} \left( \sin 8x + \sin 2x \right) \]
\[
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