Home
Class 12
MATHS
If y=cos^(-1)sqrt((sqrt(1+x^2+1))/(2sqr...

If `y=cos^(-1)sqrt((sqrt(1+x^2+1))/(2sqrt(1+x^2))),t h e n(dy)/(dx)i se q u a lto` `1/(2(1+x^2)),x in R` (b) `1/(2(1+x^2)),x >0` `(-1)/(2(1+x^2)),x<0` (d) `1/(2(1+x^2)),x<0`

A

`(1)/(2(1+x^(2))),x inR`

B

`(1)/(2(1+x^(2))),xgt0`

C

`(1)/(2(1+x^(2))),xlt0`

D

`(-1)/(2(1+x^(2))),xlt0`

Text Solution

Verified by Experts

The correct Answer is:
B, D
Put `x= tan theta`
`therefore" "tan^(-1)x in(-(pi)/(2),(pi)/(2))`
`therefore" "y=cos^(-1)sqrt((1+|sec theta|)/(2|sec theta|))`
`=cos^(-1)sqrt((cos theta+1)/(2))`
`=cos^(-1)(cos theta//2)`
`={{:(-theta//2",",-pi//2lt theta le0),(theta//2",",0lt theta ltpi//2):}`
`={{:(-(1)/(2)tan^(-1)x",",xle0),((1)/(2)tan^(-1)x",",xgt0):}`
`(dy)/(dx)={{:(-(1)/(2(1+x^(2)))",",xle0),((1)/(2(1+x^(2)))",",xgt0):}`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • METHODS OF DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|7 Videos

  • MATRICES

    CENGAGE PUBLICATION|Exercise All Questions|509 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Linked comprehension Type|2 Videos

Similar Questions

Explore conceptually related problems

If y=cos^(-1)sqrt((sqrt(1+x^2)+1)/(2sqrt(1+x^2))),t h e n(dy)/(dx) is equal to (a) 1/(2(1+x^2)),x in R (b) 1/(2(1+x^2)),x >0 (c) (-1)/(2(1+x^2)),x<0 (d) 1/(2(1+x^2)),x<0

int((x+1)dx)/(sqrt(1-2x-x^(2)))

Knowledge Check

  • Value of cos^-1 sqrt((1 + sqrt(1 + x^2))/(2sqrt(1 + x^2))) , x ge 0 is

    A
    `tan^-1 x`
    B
    `1/2 tan^-1 x`
    C
    `cot^-1 x`
    D
    `1/2 cot^-1 x`

  • If y=tan^(-1)((sqrt(1+x^(2))-1)/(x)) and z=tan^(-1)((2x)/(1-x^(2))) , then (dy)/(dz) is equal to -

    A
    `(1)/(8)`
    B
    `(1)/(4)`
    C
    `(1)/(2)`
    D
    1

    • Similar Questions

    Explore conceptually related problems

    If f(x)=sin^(-1)((sqrt(3))/2x-1/2sqrt(1-x^2)),-1/2lt=xlt=1,t h e nf(x) is equal to

    y = sin^(-1)(1/sqrt(1+x^2)) + cos^(-1)(1/sqrt(1+x^2)) . find dy/dx .

    If y = tan^(-1) ((sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))) show that (dy)/(dx) = x/sqrt(1-x^4) .

    int(sqrt(1-x^(2))-x)/(sqrt(1-x^(2))(1+xsqrt(1-x^(2))))dx is

    If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)(dy)/(dx) is equal to (a) x+y (b) 1+x y (c) 1-x y (d) x y-2

    If y = sqrt((1-cos 2x)/(1+cos 2x)) , then the value of (dy)/(dx) will be

    Home
    Profile