If `tan(A+B)p and tan(A-B)=q`, then show that `tan 2A=(p+q)/(1-pq)`

Explanation

To prove that if \( \tan(A+B) = p \) and \( \tan(A-B) = q \), then \( \tan(2A) = \frac{p + q}{1 - pq} \), we can follow these steps:

### Step 1: Express \( \tan(2A) \) in terms of \( \tan(A+B) \) and \( \tan(A-B) \)
We know that:
\[ \tan(2A) = \tan((A+B) + (A-B)) \]
This means we can express \( 2A \) as the sum of \( (A+B) \) and \( (A-B) \).
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