If `tan A+tan B=a` and `cot A+cot B=b , ` prove that: `cot(A+B)=1/a-1/b`

Explanation

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

### Step 1: Express \( \tan A \) and \( \tan B \)
From the first equation, we have:
\[ \tan A + \tan B = a \]

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