Prove that: `cot^2A-tan^2A=4 cot2A cosec2A`

Explanation

To prove the identity \( \cot^2 A - \tan^2 A = 4 \cot 2A \csc 2A \), we will follow these steps:

### Step 1: Rewrite cotangent and tangent in terms of sine and cosine
We know that:
\[ \cot A = \frac{\cos A}{\sin A} \quad \text{and} \quad \tan A = \frac{\sin A}{\cos A} \]
Thus, we can express \( \cot^2 A \) and \( \tan^2 A \):
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