If `tan(A-B)=1a n dsec(A+B)=2/(sqrt(3))` , then the smallest positive values of A and B, respectively, are `(25pi)/(24),(19pi)/(24)` (b) `(19pi)/(24),(25pi)/(24)` `(31pi)/(24),(31pi)/(24)` (d) `(13pi)/(24),(31pi)/(24)`

Explanation

To solve the problem, we need to find the smallest positive values of \( A \) and \( B \) given the equations \( \tan(A - B) = 1 \) and \( \sec(A + B) = \frac{2}{\sqrt{3}} \).

### Step 1: Solve for \( A - B \)

From the equation \( \tan(A - B) = 1 \), we know that:

\[
A - B = n\pi + \frac{\pi}{4}
...