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The smallest and the largest values of $\tan^{- 1} (\frac{1 - x}{1 + x}), 0 \leq x \leq 1$ are

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0, π

0, π4

−π4,π4

π4,π2

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Correct option is B

We have, tan−1⁡1−x1+x=tan−1⁡1−tan−1⁡x=π4−tan−1⁡xWe have, 0≤x≤1∴ 0≤tan−1⁡x≤π4⇒ 0≥−tan−1⁡x≥−π4⇒ π4≥π4−tan−1⁡x≥0⇒π4≥tan−1⁡1−x1+xx≥0

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The smallest and the largest values of tan−1⁡1−x1+x,0≤x≤1 are

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The smallest and the largest values of $\tan^{- 1} (\frac{1 - x}{1 + x}), 0 \leq x \leq 1$ are