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Question
If tan(A + B) = p, tan(A – B) = q, then show that tan 2A = `(p + q)/(1 - pq)`
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Solution
Given that: tan(A + B) = p, tan(A – B) = q
tan 2A = tan(A + B + A – B)
= tan[(A + B) + (A – B)]
= `(tan(A + B) + tan(A - B))/(1 - tan(A + B).tan(A - B))`
= `(p + q)/(1 - pq)`
Hence proved.
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