Home
Class 12
MATHS
If |cos^-1((1-x^2)/(1+x^2))| < pi/3, the...

If `|cos^-1((1-x^2)/(1+x^2))| < pi/3,` then x belongs to the interval

A

`[-1//sqrt(3),1//sqrt(3)]`

B

`(-1//sqrt(3),1//sqrt(3))`

C

`(0,1//sqrt(3))`

D

none of these

Text Solution

Verified by Experts

We have
`|cos^(-1)((1-x^(2))/(1+x^(2)))|lt(pi)/(3)` ltrbgt `rarr 1/2 lt (1-x^(2))/(1+x^(2)) lt (pi)/(3)`
`rarr 1+x^(2)lt2-2x^(2)lt2+2x^(2)`
`rarr 1+x^(2)lt2-2x^(2) and 2-2x^(2)lt2+2x^(2)`
`rarr 3x^(2)-1lt0and 4x^(2)gt0 rarr -(1)sqrt(3)ltxlt(1)/sqrt(3)`
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|11 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA|Exercise Exercise|72 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

  • INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Illustration|1 Videos

  • LIMITS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|60 Videos

Similar Questions

Explore conceptually related problems

If x<0 , then write the value of cos^(-1)((1-x^2)/(1+x^2)) in terms of tan^(-1)x

Find the derivative of y=cos^(-1)((1-x^2)/(1+x^2)) , 0

The derivative of sin^(-1)((2x)/(1+x^2)) w.r.t. cos^(-1)((1-x^2)/(1+x^2)) is equal to......

(3 sin^(-1)) ((2x)/(1+x^2)) - (4 cos^(-1)) ((1-x^2)/(1 + x^2)) + (2 tan^(-1)) ((2x)/(1-x^2)) = π/3

Define derivative of sin^(-1)((2x)/(1+x^2)) w.r.t. cos^(-1)((1-x^2)/(1+x^2)) AA\ x in Rdot

If cos^(-1)((1-x^(2))/(1+x^(2)))+sin^(-1)((2x)/(1+x^(2)))=p for all x in[-1,0] , then p is equal to

Discuss the differentiability of f(x=cos^(-1)((1-x^2)/(1+x^2))

OBJECTIVE RD SHARMA-INVERSE TRIGONOMETRIC FUNCTIONS -Section I - Solved Mcqs
  1. If 0lexle1 then sin{tan^(-1)((1-x^(2))/(2x))+cos^(-1)((1-x^(2))/(1+x^...

    Text Solution

    |

  2. If -1lexle0 then sin{tan^(-1)((1-x^(2))/(2x))-cos^(-1)((1-x^(2))/(1+x...

    Text Solution

    |

  3. If |cos^-1((1-x^2)/(1+x^2))| < pi/3, then x belongs to the interval

    Text Solution

    |

  4. The value of cos [tan^-1 {sin (cot^-1 x)}] is

    Text Solution

    |

  5. Find the value of sin^(-1)(cos(sin^(-1)x))+cos^(-1)(sin(cos^(-1)x))

    Text Solution

    |

  6. If (sin^(-1)x)^(2)+(cos^(-1)x)^(2)=(5pi^(2))/(8) then x =

    Text Solution

    |

  7. tan{(pi)/(4)+1/2cos^(-1)alpha}+tan{(pi)/(4)-1/2cos^(-1)alpha} alpha ...

    Text Solution

    |

  8. The solution set of the equation cos^(-1)x-sin^(-1)x=sin^(-1)(1-x) i...

    Text Solution

    |

  9. The number of triple satisfying sin^(-1)x+cos^(-1)y+sin^(-1)z=2pi is

    Text Solution

    |

  10. If sin^-1(sin 5)gtx^(2)-4x then

    Text Solution

    |

  11. If cos^(-1)(cos 4)gt3x^(2)-4x then

    Text Solution

    |

  12. The number of real solution (x,y) where |y|=sinx,y=cos^(-1)(cosx),-2pi...

    Text Solution

    |

  13. If u=cot^(-1)sqrt(cos theta) -tan^(-1)sqrt(cos theta) then sin u=

    Text Solution

    |

  14. tan(sec^(-1)x )=sin(cos^(-1)(1/sqrt5))

    Text Solution

    |

  15. Number of integral solutions of the equation 2 sin^-1sqrt(x^2-x +1 )+ ...

    Text Solution

    |

  16. If alpha, beta and gamma are the three angles with alpha = 2tan^(-1)(s...

    Text Solution

    |

  17. If f(x) =cos^(-1)x+cos^(-1){(x/2+1/2sqrt(3-3x^(2)))} then f(2/3) equ...

    Text Solution

    |

  18. The trigonometric equation sin^(-1)x=2sin^(-1)a has a solution for all...

    Text Solution

    |

  19. If alpha is the only real root of the equation x^3 + bx^2 + cx + 1 = ...

    Text Solution

    |

  20. If tan^(-1)(a/x)+tan^(-1)(b/x)+tan^(-1)(c /x)+tan^(-1)(d/x)=(pi)/(2) t...

    Text Solution

    |