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If alphain(0,pi/2) then sqrt(x^2+x)+(tan...

If `alphain(0,pi/2)` then `sqrt(x^2+x)+(tanalpha)^2/(sqrt(x^2+x))` is always greater than or equal to

A

`2 tan alpha`

B

2

C

1

D

`sec^(2) alpha`

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Knowledge Check

  • Value of sqrt(x^(2)+x)+(tan^(2)alpha)/(sqrt(x^(2)+x)),xgt0,alpha in (0,(pi)/2) is always greater than or equal to

    A
    2
    B
    `5//2`
    C
    `2 tan alpha`
    D
    `sec alpha`

  • Let a in (0,(pi)/(2)) and f(x)=sqrt(x^(2)+x)+(tan^(2)alpha)/(sqrt(x^(2)+x)), x gt 0 . If the least value of f(x) is 2sqrt3 , then alpha is equal to

    A
    `(pi)/(3)`
    B
    `(pi)/(8)`
    C
    `(pi)/(6)`
    D
    `(pi)/(4)`

  • If sqrt(x) + (1)/(sqrt(x)) = 2sqrt(2) , then x^(2) + (1)/(x^(2)) is equal to :

    A
    34
    B
    64
    C
    36
    D
    32

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