If `A+B+C=pi` , prove that `cotA+cotB+cotC-cos e cAdotcos e cBdotcos e cC=cotAdotcotBdotcotCdot`

Explanation

To prove the equation \( \cot A + \cot B + \cot C - \cos A \cos B \cos C = \cot A \cot B \cot C \) given that \( A + B + C = \pi \), we will start with the left-hand side and manipulate it step by step.

### Step 1: Rewrite cotangent in terms of sine and cosine
We know that:
\[ \cot A = \frac{\cos A}{\sin A}, \quad \cot B = \frac{\cos B}{\sin B}, \quad \cot C = \frac{\cos C}{\sin C} \]
Thus, we can express the left-hand side as:
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