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$4 \tan^{- 1} \frac{1}{5} - \tan^{- 1} \frac{1}{239}$ is equal to

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a

π

b

π/2

c

π/3

d

π/4

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detailed solution

Correct option is D

We have, 4tan−1⁡15−tan−1⁡1239= 2tan−1⁡2/51−1/25−tan−1⁡1239= 2tan−1⁡(5/12)−tan−1⁡1/239= tan−1⁡2(5/12)1−(5/12)2−tan−1⁡1239= tan−1⁡120119−tan−1⁡1239= tan−1⁡120/119−1/2391+120/119×1/239= tan−1⁡2856928569=tan−1⁡(1)=π4

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