If in a `!ABC` , a = 6 , b = 3 and cos (A -B) =`4/5`,then its area in square units, is

Options

A. 8
B. 9
C. 6
D. none of these

Explanation

To find the area of triangle ABC, given that \( a = 6 \), \( b = 3 \), and \( \cos(A - B) = \frac{4}{5} \), we can follow these steps:

### Step 1: Use the formula for \( \tan \left( \frac{A - B}{2} \)

We know that:
\[ \tan \left( \frac{A - B}{2} \right) = \sqrt{\frac{1 - \cos(A - B)}{1 + \cos(A - B)}} \]
...