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Question
If tan (A + B) = p and tan (A − B) = q, then write the value of tan 2B.
Solution
\[\tan 2B = \tan(B + B)\]
\[ = \tan(A + B - (A - B))\]
\[ = \frac{\tan(A + B) - \tan(A - B)}{1 + \tan(A + B)\tan(A - B)} \]
\[ = \frac{p - q}{1 + pq} \left[ \because \tan(A + B) = p \text{ and } \tan(A - B) = q \right]\]
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