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tan^(-1)""(m)/(n)-tan^(-1)""(m-n)/(m+n) ...

`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))`

A

`tan^(-1)""(n)/(m)`

B

`tan^(-1)""(m+n)/(m-n)`

C

`(pi)/(4)`

D

`tan^(-1)((1)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • The value of tan^(-1)((sqrt(3))/(2))+tan^(-1)((1)/(sqrt(3))) is equal to a) tan^(-1)((5)/(sqrt(3))) b) tan^(-1)((2)/(sqrt(3))) c) tan^(-1)((1)/(2)) d) tan^(-1)((1)/(3sqrt(3)))

    A
    `tan^(-1)((5)/(sqrt(3)))`
    B
    `tan^(-1)((2)/(sqrt(3)))`
    C
    `tan^(-1)((1)/(2))`
    D
    `tan^(-1)((1)/(3sqrt(3)))`

  • 2"tan"^(-1)(1/(3))+"tan"^(-1)(1/(4)) is equal to

    A
    `"tan"^(-1)(16/(13))`
    B
    `"tan"^(-1)(17/(23))`
    C
    `pi/(4)`
    D
    0

  • If a_(1), a_(2), a_(3), ………., a_(n) are in AP with common difference 5 and if a_(i)a_(j) ne -1 for i, j = 1, 2, …….., n, then tan^(-1)((5)/(1+a_(1)a_(2))) + tan^(-1)((5)/(1+a_(2)a_(3))) +……..+ tan^(-1)((5)/(1+a_(n-1)a_(n))) is equal to a) tan^(-1)((5)/(1+a(n)a_(n-1))) b) tan^(-1)((5)/(1+a(n)a_(n))) c) tan^(-1)((5n-5)/(1+a(n)a_(n+1))) d) tan^(-1)((5n-5)/(1+a_(1)a_(n)))

    A
    `tan^(-1)((5)/(1+a(n)a_(n-1)))`
    B
    `tan^(-1)((5)/(1+a(n)a_(n)))`
    C
    `tan^(-1)((5n-5)/(1+a(n)a_(n+1)))`
    D
    `tan^(-1)((5n-5)/(1+a_(1)a_(n)))`

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