If `tanA-tanB=x a n dcotB-cotA=y ,` prove that `cot(A-B)=1/x+1/y`

Explanation

To prove that \( \cot(A - B) = \frac{1}{x} + \frac{1}{y} \) given that \( \tan A - \tan B = x \) and \( \cot B - \cot A = y \), we can follow these steps:

### Step 1: Write down the given conditions
We have:
1. \( \tan A - \tan B = x \) (1)
2. \( \cot B - \cot A = y \) (2)

### Step 2: Rewrite the second condition in terms of tangent
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