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Considering only the principal values of the inverse trigonometric functions, the value of
`(3)/(2) cos^(-1) sqrt((2)/(2 + pi^(2))) + (1)/(4) "sin"^(-1) "" (2sqrt2 pi)/(2 + pi^(2)) + "tan"^(-1) "" (sqrt2)/(pi)` is ____________.

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Knowledge Check

  • Considering only the principal values of the inverse functions, the set A = {x ge 0, tan^(-1)(2x) + tan^(-1)(3x) = pi//4}

    A
    is an empty set
    B
    contains more than two elements
    C
    contains two elements
    D
    is a singleton

  • Considering only the principal values of inverse functions, the set A={x ge 0 :tan^(-1)(2x)+tan^(-1)(3x)=(pi)/(4)}

    A
    Is an empty set
    B
    Contains two elements
    C
    Contains more than two elements
    D
    Is a singleton

  • Considering only the principal values of inverse trigonometric functions,the number of positive real values of "x" satisfying tan^(-1)(x)+tan^(-1)(2x)=(pi)/(4) is

    A
    more than 2
    B
    2
    C
    0
    D
    1

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