Question

If $\tan A + \tan B = m$ and $\tan A \tan B = n$, then $\tan(A + B)$ is: 

• A. $\frac{m+n}{1-mn}$
• B. $\frac{m}{1-n}$
• C. $\frac{m-n}{1+mn}$
• D. $\frac{m}{1+n}$

Hint:

• Recall the tangent addition formula: \(\tan(X+Y) = \frac{\tan X + \tan Y}{1 - \tan X \tan Y}\).
• Directly substitute the given expressions for \((\tan A + \tan B)\) and \((\tan A \tan B)\) into this formula.

Answer 1

The Correct Option is B

We use the tangent addition formula: 
$\tan(A+B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}$. 
Given: $\tan A + \tan B = m$. $\tan A \tan B = n$. 
Substitute these into the formula for $\tan(A+B)$: $\tan(A+B) = \frac{m}{1 - n}$. 
This matches option (b). \[ \boxed{\frac{m}{1-n}} \]