Home
Class 12
MATHS
Given 0 le x le 1/2, then the value of :...

Given `0 le x le 1/2`, then the value of : `tan[sin^-1(x/sqrt2 + (sqrt(1-x^2))/sqrt2)- sin^-1x]` is

A

1) 1

B

2) `sqrt3`

C

3) `-1`

D

4) `1/sqrt3`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • INVERSE-TRIGONOMETRIC FUNCTIONS

    MODERN PUBLICATION|Exercise EXERCISE|111 Videos
  • INTEGRALS

    MODERN PUBLICATION|Exercise EXERCISE|768 Videos
  • LINEAR PROGRAMMING

    MODERN PUBLICATION|Exercise EXERCISE|156 Videos

Similar Questions

Explore conceptually related problems

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

Differentiate tan^-1 (x/(sqrt(1-x^2))) w.r.t. sin^-1 x .

Prove that tan^(-1)((x)/(1+sqrt(1-x^(2))))=(1)/(2)sin^(-1)x .

Differentiate sin^-1 (x/(sqrt(1+x^2))) w.r.t. tan^-1 x .

Prove that : 2 sin^-1 x = sin^-1 (2x sqrt(1-x^2)), |x| le (1/(sqrt2)

Integrate the function: (sin^(-1)x)/sqrt(1-x^2)

If sin^(-1)x_i in [0,1]AAi=1,2,3, .28 then find the maximum value of sqrt(sin^(-1)x_1)sqrt(cos^(-1)x_2)+sqrt(sin^(-1)x_2)sqrt(cos^(-1)x_3)+ sqrt(sin^(-1)x_3)sqrt(cos^(-1)x_4)+....+sqrt(sin^(-1)x_(28))sqrt(cos^(-1)x_1)

Find dy/dx in the following: y=sin^-1(2x sqrt(1-x^2)) , -1/sqrt2ltxlt1/sqrt2

Prove that tan^-1(x/(sqrt(a^2 - x^2)) = sin^-1 (x/a), |x| < a.

Range of f(x) =sin^-1(sqrt(x^2+x+1)) is

MODERN PUBLICATION-INVERSE-TRIGONOMETRIC FUNCTIONS-EXERCISE
  1. The value of sec^2 (tan^(-1)3) + cosec^2(cot^-1 2) is

    Text Solution

    |

  2. If sin^-1(x/13) + cosec^-1(13/12) = pi/2 then the value of x is

    Text Solution

    |

  3. Given 0 le x le 1/2, then the value of : tan[sin^-1(x/sqrt2 + (sqrt(1-...

    Text Solution

    |

  4. The value of sin(2 sin^(-1)0.8) is equal to

    Text Solution

    |

  5. The value of tan^-1(sqrt3/2) + tan^-1(1/sqrt3) is equal to

    Text Solution

    |

  6. The value of cos(sin^-1(2/3)) is equal to

    Text Solution

    |

  7. If tan^-1 2x + tan^-1 3x = pi/2, then the value of x is equal to

    Text Solution

    |

  8. If sin^-1x + sin^-1 y + sin^-1z = (3pi)/2, then the value of x^9 + y^9...

    Text Solution

    |

  9. 2 cos^-1 x = sin^-1(2xsqrt(1-x^2)) is valid for all value of x satisfy...

    Text Solution

    |

  10. The number of real solutions of the equations: tan^-1 sqrt(x(x+1)) + s...

    Text Solution

    |

  11. If cos^-1 x - cos^-1 y/2 = alpha, then 4x^2 - 4xy cos alpha + y^2 is e...

    Text Solution

    |

  12. If sin^-1(x/5) + cosec^-1(5/4)= pi/2, then a value of x is

    Text Solution

    |

  13. The value of cot(cosec^-1(5/3) + tan^-1(2/3) is

    Text Solution

    |

  14. If 0 < x < 1, then : sqrt(1+x^1)[{ x cos(cot^-1x) + sin (cot^-1 x}^2 -...

    Text Solution

    |

  15. If tan^(-1) y = tan^(-1) x + tan^(-1)((2x)/(1 -x^(2)))", where" |x| lt...

    Text Solution

    |

  16. Find the value of sin^-1(sin(4pi)/5)

    Text Solution

    |

  17. show that: 2 sin^-1(3/5) = tan^-1(24/7)

    Text Solution

    |

  18. Write the value of tan^(-1)[2sin(2cos^(-1)""sqrt(3)/2)].

    Text Solution

    |

  19. show that tan^-1(1/2) + tan^-1(1/5) + tan^-1(1/8) = pi/4

    Text Solution

    |

  20. If tan^-1((x-2)/(x-4)) + tan^-1((x+2)/(x+4)) = pi/4 find the value of ...

    Text Solution

    |