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Prove that 1/(1+p+q^(- 1))+1/(1+q+r^(- 1...

Prove that `1/(1+p+q^(- 1))+1/(1+q+r^(- 1))+1/(1+r+p^(- 1))=1,if pqr=1` .

Answer

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Prove tan ^ (- 1) ((1) / (p + q)) + tan ^ (- 1) ((a) / (p ^ (2) + q + 1)) = cos ^ (- 1) p

If the lengths of the perpendiculars from the vertices of a triangle ABC on the opposite sides are p_(1), p_(2), p_(3) then prove that (1)/(p_(1)) + (1)/(p_(2)) + (1)/(p_(3)) = (1)/(r) = (1)/(r_(1)) + (1)/(r_(2)) + (1)/(r_(3)) .

Knowledge Check

  • The value of 1/(1+p+q^(1)) + 1/(1+q+r^-(1)) + 1/(1+r+p^(-1)), given that pqr = 1 is :

    A
    1
    B
    0
    C
    (p+q+r)-1
    D
    p+q+r

  • The value of 1/(p + q^(-1) + 1) + 1/(q + r^(-1) + 1) + 1/(1 + r + p^(-1)) given that pqr = 1 is :

    A
    1
    B
    0
    C
    pqr
    D
    p+q+r

  • If pqr = 1, then ((1)/(1+p+q^(-1))+(1)/(1+q+r^(-1))+(1)/(1+r+p^(-1))) is equal to

    A
    1
    B
    pq
    C
    qr
    D
    `(1)/(pq)`

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