Home
Class 12
MATHS
A value of x satisfying tan(sec^(-1)x...

A value of x satisfying
`tan(sec^(-1)x)=sin(cos^(-1).(1)/sqrt5)` is

A

`pm sqrt(5)/(3)`

B

`pm (3)/sqrt(5)`

C

`pm sqrt(3)/(5)`

D

`pm 3/5`

Text Solution

Verified by Experts

The correct Answer is:
D
We have
`tan(sec^(-1)x)=sin(cos^(-1)(1)/sqrt(5))`
`rarr sqrt(sec^(2)(sec^(-1)x)-1)=sin(sin^(-1))(2)/sqrt(5)`
`rarr sqrt(x^(-1))=(2)/sqrt(5)rarrx=pm (3)/sqrt(5)`
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

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

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|72 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • LIMITS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos

Similar Questions

Explore conceptually related problems

Value of x satisfying tan(sec^(- 1)x)=sin(cos^(- 1)(1/(sqrt(5))))

tan(sec^(-1) (1/x))=sin(cos^(-1) (1/sqrt(5)))

The value(s) of x satisfying tan^(-1)(x+3)-tan^(-1)(x-3)=sin^(-1)(3/5) may be

The set of value of x, satisfying the equation tan^(2)(sin^(-1)x) gt 1 is :

The number of integral values of x satisfying the equation tan^(-1) (3x) + tan^(-1) (5x) = tan^(-1) (7x) + tan^(-1) (2x) is ____

Find the value of x which satisfy equation 2 tan^(-1) 2x = sin^(-1).(4x)/(1 + 4x^(2))

Value of tan^(- 1){sin(cos^(- 1)sqrt(2/3))} is

The set of values of x, satisfying the equation tan^2(sin^-1x) > 1 is -

The value of x satisfying the equation cos^(-1)3x+sin^(-1)2x=pi is

If the value of x satisfying the equation sin^(-1)sqrt(1-x^2)=tan^(-1)sqrt(2/x-1) is a/b (where a&b are coprime), then the value of a^2+b^2 is a. 7 b. 5 c. 3 d. 1

OBJECTIVE RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS -Section I - Solved Mcqs
  1. The number of solution of sin{sin^(-1)(log(1//2)x)}+2|cos{sin^(-1)(x...

    Text Solution

    |

  2. The value of "tan"(sin^(-1)("cos"(sin^(-1)x)))"tan"(cos^(-1)(sin(cos^(...

    Text Solution

    |

  3. A value of x satisfying tan(sec^(-1)x)=sin(cos^(-1).(1)/sqrt5) is

    Text Solution

    |

  4. Exhaustive set of values of parameter 'a' so that sin^(-1)x-tan^(-1)x=...

    Text Solution

    |

  5. If a le sin^(-1)x +cos^(-1)x+tan^(-1)x le b, then:

    Text Solution

    |

  6. If -1lexle0 then sin^(-1)x equals

    Text Solution

    |

  7. If tan^(-1) ((x+1)/(x-1))+tan^(-1)((x-1)/x)=tan^(-1)(-7) , then the va...

    Text Solution

    |

  8. Using mathematical induction , prove that tan^(-1)((1)/(3))+tan^(-1)((...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. sin [ tan^(-1). (1 - x^(2))/(2x) + cos^(-1) . (1-x^(2))/(1 + x^(2))] i...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. Find the value of, cos [tan^(-1) {sin (cot^(-1)x)}]

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. tan ((pi)/(4) + (1)/(2) cos^(-1) x) + tan ((pi)/(4) - (1)/(2) cos^(-1)...

    Text Solution

    |

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

    Text Solution

    |

  19. Number of triplets (x, y, z) satisfying sin^(-1)x+cos^(-1)y+sin^(-1)z=...

    Text Solution

    |

  20. The complete set of values of x satisfying the inequality sin^(-1)(si...

    Text Solution

    |