Question

If tan (A + B) = p and tan (A − B) = q, then write the value of tan 2B.

Answer 1

$$\begin{gathered} \tan 2B=\tan (B+B) \\ =\tan (A+B-(A-B\left)\right) \\ =\frac{\tan (A+B)-\tan (A-B)}{1+\tan (A+B)\tan (A-B)} \\ =\frac{p-q}{1+pq}\left[\because \tan (A+B)=p\mathrm{and}\tan (A-B)=q\right] \end{gathered}$$