• # question_answer If $\tan \,(A+B)=p,\,\,\tan \,(A-B)=q,$ then the value of $\tan \,2A$ in terms of p and q is [MP PET 1995, 2002] A) $\frac{p+q}{p-q}$ B) $\frac{p-q}{1+pq}$ C) $\frac{p+q}{1-pq}$ D) $\frac{1+pq}{1-p}$

$2A=(A+B)+(A-B)$ $\Rightarrow$$\tan 2A=\frac{\tan (A+B)+\tan (A-B)}{1-\tan (A+B)\tan (A-B)}=\frac{p+q}{1-pq}$.