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If f (x) = tan ^(-1)sqrt((1 + sin x )/(1...

If `f (x) = tan ^(-1)sqrt((1 + sin x )/(1 - sin x)), 0 le x le (pi)/(2) then f' ((pi)/(6))` =?

A

`1//2`

B

`-1//2`

C

1

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
B
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Knowledge Check

  • if f(x) = tan^(-1) "" sqrt""[(1+ sin x ]// (1- sin x )], 0 le x le x pi//2 then f'(pi //6) is

    A
    `-1/4`
    B
    `-1/2`
    C
    `1/4`
    D
    `1/2`

  • If f(x)=tan^(-1)sqrt((1+sinx)//(1-sinx)),0le x lt pi//2 , then f'(pi//6) is

    A
    `-1//4`
    B
    `-1//2`
    C
    `1//4`
    D
    `1//2`

  • Let f(x) = 1 + 2 sin x + 2 cos^2 x, 0 le x le pi//2 . Then

    A
    f (x) is greatest at `pi//6`
    B
    least at `0, pi//2`
    C
    increasing in `[0,pi//6]` and decreasing in `(pi//6, pi//2)`
    D
    f(x) is continuous in `[0,pi//2]`

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