Question:
If $\tan A + \tan B = m$ and $\tan A \tan B = n$, then $\tan(A + B)$ is:
If $\tan A + \tan B = m$ and $\tan A \tan B = n$, then $\tan(A + B)$ is:
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- 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.
Updated On: Mar 18, 2026
- $\frac{m+n}{1-mn}$
- $\frac{m}{1-n}$
- $\frac{m-n}{1+mn}$
- $\frac{m}{1+n}$
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The Correct Option is B
Solution and Explanation
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). \[ \boxed{\frac{m}{1-n}} \]
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