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If tan(A+B)=p and tan(A-B)=q, then show...

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

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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: Write the expression for \( \tan(2A) \) We know that: \[ \tan(2A) = \tan(A + A) = \frac{\tan A + \tan A}{1 - \tan A \tan A} = \frac{2\tan A}{1 - \tan^2 A} \]
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