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If $x, y > 0, then \tan^{- 1} (\frac{x}{y}) - \tan^{- 1} (\frac{x - y}{x + y})$ is

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π2

π3

π4

π4 or −3π4

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detailed solution

Correct option is C

We have,tan−1⁡xy−tan−1⁡x−yx+y=tan−1⁡xy−tan−1⁡1−y/x1+y/x=tan−1⁡xy−tan−1⁡1−tan−1⁡yx=tan−1⁡xy+tan−1⁡yx−π4=tan−1⁡xy+cot−1⁡xy−π4=π2−π4=π4

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If x,y>0, then tan−1⁡xy−tan−1⁡x−yx+y is

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If $x, y > 0, then \tan^{- 1} (\frac{x}{y}) - \tan^{- 1} (\frac{x - y}{x + y})$ is