If `tan^(-1)x+tan^(-1)y=pi/4,` then write the value of `x+y+x ydot`

Explanation

To solve the equation \( \tan^{-1}x + \tan^{-1}y = \frac{\pi}{4} \) and find the value of \( x + y + xy \), we can follow these steps:

### Step 1: Use the formula for the sum of inverse tangents
We know the formula:
\[ \tan^{-1}a + \tan^{-1}b = \tan^{-1}\left(\frac{a + b}{1 - ab}\right) \]
In our case, we can apply this formula by letting \( a = x \) and \( b = y \):
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