For the next two (02) items that follow : Given that \(\tan\left(\dfrac{A}{2}+\dfrac{B}{2}\right)=p\) and \(\tan\left(\dfrac{A}{2}-\dfrac{B}{2}\right)=q\), where \(pq\neq\pm1\).
What is \(\tan A\) equal to?
\(\dfrac{p+q}{1-pq}\)
Since \(A=\left(\dfrac{A}{2}+\dfrac{B}{2}\right)+\left(\dfrac{A}{2}-\dfrac{B}{2}\right)\), applying the tangent addition formula gives \(\tan A=\dfrac{p+q}{1-pq}\).
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