`tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y))`is equal to (A) `pi/2` (B) `pi/3` (C) `pi/4` (D) `(-3pi)/4`

Explanation

To solve the expression \( \tan^{-1}\left(\frac{x}{y}\right) - \tan^{-1}\left(\frac{x-y}{x+y}\right) \), we can use the formula for the difference of inverse tangents:

\[ \tan^{-1}(a) - \tan^{-1}(b) = \tan^{-1}\left(\frac{a - b}{1 + ab}\right) \]

Let:
- \( a = \frac{x}{y} \)
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