Question

If $\tan (A+B)=p,\tan (A-B)=q,$ then the value of $\tan 2A$ in terms of p and q is given by

• A. $\frac{p+q}{p-q}$
• B. $\frac{p-q}{1+pq}$
• C. $\frac{p+q}{1-pq}$
• D. $\frac{1+pq}{1-p}$

Answer 1

The correct option is C $\frac{p+q}{1-pq}$

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