If `tan(A-B)=x` , then the value of x is

Options

A. `((tanA+tanB))/((1-tanAtanB))`
B. `((tanA+tanB))/((1+tanAtanB))`
C. `((tanA-tanB))/((1-tanAtanB))`
D. `((tanA-tanB))/((1+tanAtanB))`

Answer

To solve the problem where we need to find the value of \( x \) given that \( \tan(A - B) = x \), we can follow these steps:

### Step 1: Write the formula for \( \tan(A - B) \)
The formula for the tangent of a difference is given by:
\[ \tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B} \]
Thus, we can express \( x \) as:
\[ x = \tan(A - B) \]

### Step 2: Substitute the formula into the equation
By substituting the formula into our expression for \( x \), we have:
\[ x = \frac{\tan A - \tan B}{1 + \tan A \tan B} \]

### Step 3: Identify the components
In this expression:
- The numerator is \( \tan A - \tan B \)
- The denominator is \( 1 + \tan A \tan B \)

### Step 4: Final expression
Thus, we can conclude that the value of \( x \) is:
\[ x = \frac{\tan A - \tan B}{1 + \tan A \tan B} \]

### Conclusion
This is the final result for \( x \) in terms of \( \tan A \) and \( \tan B \).

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