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