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

Question

If $\tan(\text{A+B})=\text{p}$ and $\tan\text{(A - B)}=\text{q},$ then write the value of $\tan2\text{B}.$

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Answer

We have,
$\tan(\text{A+B})=\text{p}$ and $\tan(\text{A - B})=\text{q}$
Now, $\tan2\text{B}=\tan\big[(\text{A+B})-(\text{A}-\text{B})\big]$
$=\frac{\tan(\text{A+B})-\tan\text{(A - B)}}{1+\tan(\text{A+B})\times\tan(\text{A - B})}$
$=\frac{\text{p - q}}{1+\text{pq}}$
$\therefore\ \tan2\text{B}=\frac{\text{p - q}}{1+\text{pq}}$

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