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Prove that tan^-1 (1/2)+tan^-1(2/11)=...

Prove that
`tan^-1 (1/2)+tan^-1(2/11)=tan^-1(3/4)`

Answer

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Knowledge Check

  • If alpha = tan^(-1)(1)+1/2tan^(-1)(2) +1/3 tan^(-1)(3), beta = tan^(-1) (1) + 2tan^(-1)(1/2) +3 tan^(-1)(1/3) , then |alpha - beta| =

    A
    `(5pi)/24+5/6 cot^(-1)3`
    B
    `(5pi)/24+1/6cot^(-1)3`
    C
    `(7pi)/24+1/6cot^(-1)3`
    D
    `(11pi)/24+1/6cot^(-1)3`
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