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The value of $\tan^{- 1} (\frac{1}{2} \tan 2 A) + \tan^{- 1} (\cot A) + \tan^{- 1} (\cot^{3} A)$ , for $0 < A < π / 4$ , is

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tan−12

tan−1(cotA)

4tan−1(1)

2tan−1(2)

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detailed solution

Correct option is C

For 01⇒(cotA)(cot3A)>1⇒tan−1(12tan2A)+tan−1(cotA)+tan−1(cot3A)=tan−1(tanA1−tan2A)+π+tan−1(cotA+cot3A1−cot4A)=tan−1(tanA1−tan2A)+π+tan−1(cotA1−cot2A)=tan−1(tanA1−tan2A)+π+tan−1(tanAtan2A−1)=π=4(π/4)=4tan−1(1)

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The value of tan−1(12tan2A)+tan−1(cotA)+tan−1(cot3A) , for 0<A<π/4 , is

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The value of $\tan^{- 1} (\frac{1}{2} \tan 2 A) + \tan^{- 1} (\cot A) + \tan^{- 1} (\cot^{3} A)$ , for $0 < A < π / 4$ , is