Question:
If tan (A + B) = p, tan (A – B) = q, then the value of tan 2A in terms of p and q is ___________.
Solution:
Given (A + B) = p
tan (A – B) = q
$\tan 2 A=\tan [A+A]$
$=\tan [(A+B)+(A-B)]$
$=\frac{\tan (A+B)+\tan (A-B)}{1-\tan (A+B) \tan (A-B)} \quad\left[\right.$ using identity $\left.\tan (x+y)=\frac{\tan x+\tan y}{1-\tan x \tan y}\right]$
$\tan 2 A=\frac{p+q}{1-p q}$
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