Home
Class 12
MATHS
if tan^-1 {(sqrt(1+x^2)-sqrt(1-x^2))/(sq...

if `tan^-1 {(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))}=alpha` then `x^2` is:

A

sin 2 `alpha`

B

sin 2 `alpha`

C

cos 2 `alpha`

D

cos `alpha`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • GGSIPU MATHEMATICS 2009

    IPUCET PREVIOUS YEAR PAPERS|Exercise MCQs|47 Videos

  • GGSIPU MATHEMATICS 2014

    IPUCET PREVIOUS YEAR PAPERS|Exercise MCQs|45 Videos

Similar Questions

Explore conceptually related problems

If tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))}=alpha , then x^2= sin2\ alpha (b) sin\ alpha (c) cos2\ alpha (d) cos\ alpha

If tan^(-1){(sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1-x^(2))+sqrt(1-x^(2)))}=alpha, then prove that x^(2)=sin2 alpha

If y=tan^(-1) ((sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))), x^2 le 1 , then find (dy)/(dx)

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

Differentiate tan^(-1){(sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2)))} with respect to cos^(-1)x^(2)

lim_(x rarr0)(sqrt(1-x)-sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1+x))

If y=tan^(-1){(sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))} , -1 < x < 1, x!= 0 . Find dy/dx .

IPUCET PREVIOUS YEAR PAPERS-GGSIPU MATHEMATICS 2010-MCQs
  1. A skew symmetric matrix S satisfies the relations S^(2)+1=0 where I i...

    Text Solution

    |

  2. A die is loaded so that the probability of a face i is proportional...

    Text Solution

    |

  3. if tan^-1 {(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))}=alpha ...

    Text Solution

    |

  4. tan((pi)/(4) +(1)/(2)"cos"^(-1)(a)/(b))+ tan((pi)/(4) - (1)/(2)"cos"^(...

    Text Solution

    |

  5. In a triangleABC, A :B:C= 3:5:4. Then a+b+csqrt(2) is equal to

    Text Solution

    |

  6. The set of values of x for which (tan 3x - tan 2x)/(1+ tan 3x tan 2x) ...

    Text Solution

    |

  7. Which of the two 3x-4y+4=0 and 3x-3y+12=0 is nearer to origin

    Text Solution

    |

  8. If the equal sides AB and AC (each equal to 5 units) of a right-angled...

    Text Solution

    |

  9. A variable circule having fixed radius 'a' passes through origin and m...

    Text Solution

    |

  10. Find the condition that the straight line cx-by+b^2=0 may touch the ci...

    Text Solution

    |

  11. If two circles (x-1)^(2)+(y-3)^(2)=r^(2) and x^(2)+y^(2)-8x+2y+8=0 int...

    Text Solution

    |

  12. Find the number of distinct normals that can be drawn from (-2,1) to t...

    Text Solution

    |

  13. If parabolas y^2=lambdax and 25[(x-3)^2+(y+2)^2]=(3x-4y-2)^2 are equal...

    Text Solution

    |

  14. The eccentricity of an ellipse whose pair of a conjugate diameter are ...

    Text Solution

    |

  15. If the foci of the ellipse (x^2)/(16)+(y^2)/(b^2)=1 and the hyperbola ...

    Text Solution

    |

  16. The number of vectors of unit length perpendicular to the vectors hat...

    Text Solution

    |

  17. If veca=hati+hatj+hatk, vecb=4hati+3hatj+4hatk and vecc=hati+alphahatj...

    Text Solution

    |

  18. Let the pairs |hati|hatb| and |hatc,hatd| each determines a plane the...

    Text Solution

    |

  19. The equation of the plane perpendicular to the yz plnae and passing th...

    Text Solution

    |

  20. If the planes hatr.2hati+gammahatj-3hatk=0 and hatr.gamma hati+3hatj+h...

    Text Solution

    |