Question

If tan(A+B) =p and tan(A-B) = q, then write the value of tan2B.

Answer 1

We have,
tan(A+B)=p and tan(A-B)=q
Now, tan2B=tan[(A+B)-(A-B)]
$=\frac{tan(A+B)-tan(A-B)}{1+tan(A+B)\times tan(A-B)}$
$=\frac{p-q}{1+pq}$
$\therefore tan2B=\frac{p-q}{1+pq}$