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tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y))is eq...

`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`

Text Solution

AI Generated Solution

To solve the expression \( \tan^{-1}\left(\frac{x}{y}\right) - \tan^{-1}\left(\frac{x-y}{x+y}\right) \), we can use the properties of inverse tangent functions. ### Step-by-Step Solution: 1. **Use the formula for the difference of two inverse tangents**: The formula for the difference of two inverse tangents is given by: \[ \tan^{-1}(a) - \tan^{-1}(b) = \tan^{-1}\left(\frac{a - b}{1 + ab}\right) ...
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