Prove that: `(sin9A-sin7A)/(cos7A-cos9A)=cot8A`

Explanation

To prove that \(\frac{\sin 9A - \sin 7A}{\cos 7A - \cos 9A} = \cot 8A\), we will start with the left-hand side (LHS) and manipulate it using trigonometric identities.

### Step 1: Apply the sine difference formula
The sine difference formula states that:
\[ \sin x - \sin y = 2 \cos\left(\frac{x+y}{2}\right) \sin\left(\frac{x-y}{2}\right) \]
For our case, let \(x = 9A\) and \(y = 7A\):
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