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Prove that: "tan"^(-1)(m)/(n)-tan^(-1)((...

Prove that: `"tan"^(-1)(m)/(n)-tan^(-1)((m-n)/(m+n))=(pi)/(4). m, n gt 0`

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Prove that: tan^(-1)((m)/(n))+tan^(-1)((n-m)/(n+m))=[(pi)/(4)(m)/(n)>;-1(-3 pi)/(4)(m)/(n)<-1

If tan ^(-1) ((1)/(2)) + tan ^(-1) ((2)/(3x)) + tan ^(-1) ((3)/(4)) = (pi)/(2), then the value of sin (pi - 2 tan ^(-1) x) is (m)/(n), where m and n are natural numbers, n coprime to each other, then (n + m) is

Knowledge Check

  • tan^(-1)(m/n)-tan^(-1)((m-n)/(m+n)) is equal to

    A
    `tan^(-1)(n/m)`
    B
    `tan^(-1)((m+n)/(m-n))`
    C
    `pi/4`
    D
    `tan^(-1)(1/2)`

  • What is the value of tan^(-1)((m)/(n))-tan^(-1)((m-n)/(m+n)) ?

    A
    `pi`
    B
    `(pi)/(2)`
    C
    `(pi)/(4)`
    D
    `(pi)/(3)`

  • What is the value of tan^(-1)((m)/(n))-tan^(-1)((m-n)/(m+n))?

    A
    `pi`
    B
    `(pi)/(2)`
    C
    `(pi)/(4)`
    D
    `(pi)/(3)`

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    Prove that: sum_(m=1)^(n)tan^(-1)((2m)/(m^(4)+m^(2)+2))=tan^(-1)((n^(2)+n)/(n^(2)+n+2))

    (tan^(-1)((1)/(3))+tan^(-1)((1)/(7))+tan^(-1)((1)/(13))+......+tan^(-1)((1)/(381)))=(m)/(n) where m,n in N, then find least value of (m+n)

    If the sum sum_(n=1)^(10)sum_(m=1)^(10)tan^(-1)((m)/(n))=k pi, find the value of k

    Statement 1: If agt0,bgt0, tan^(-1)(a/x)+tan^(-1)(b/x)=(pi)/2 . implies x=sqrt(ab) Statement 2: If m,n epsilonN,ngem, then "tan"^(-1)(m/n)+tan^(-1)(n-m)/(n+m)=(pi)/4 .

    sum_(n=1)^(n) tan^(-1) (2m)/(m^(4) + m^(2) + 2) =

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