$$ an ( A + B ) = \frac { an A + an B } { 1 - an A an B } $$

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$$ 	an ( A + B ) = \frac { 	an A + 	an B } { 1 - 	an A 	an B } $$

UpStudy AI · Accepted Answer

The equation you've provided is the formula for the tangent of the sum of two angles, $$ A $$ and $$ B $$. This formula is useful in trigonometry for simplifying expressions involving the tangent function.

To understand this formula better, let's break it down step by step:

1. **Understanding the Components**:
   - $$ \tan A $$ and $$ \tan B $$ are the tangents of angles $$ A $$ and $$ B $$, respectively.
   - The right side of the equation combines these two tangents in a specific way.

2. **Formula Explanation**:
   - The left side, $$ \tan (A + B) $$, represents the tangent of the sum of angles $$ A $$ and $$ B $$.
   - The right side, $$ \frac{\tan A + \tan B}{1 - \tan A \tan B} $$, shows how to compute this tangent using the individual tangents of $$ A $$ and $$ B $$.

3. **Conditions for Validity**:
   - This formula is valid as long as $$ 1 - \tan A \tan B \neq 0 $$. If $$ \tan A \tan B = 1 $$, the formula would involve division by zero, which is undefined.

4. **Applications**:
   - This formula is often used in problems involving angle addition in trigonometry, such as solving equations or simplifying expressions.

If you have a specific problem or application in mind regarding this formula, please provide more details, and I can assist you further!
The formula for the tangent of the sum of two angles $$ A $$ and $$ B $$ is: $$ \tan (A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} $$ This formula helps in calculating $$ \tan (A + B) $$ using the individual tangents of $$ A $$ and $$ B $$, provided that $$ 1 - \tan A \tan B \neq 0 $$.

\( \tan ( A + B ) = \frac { \tan A + \tan B } { 1 - \tan A \tan B } \)

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