Home
Class 12
MATHS
If y=x^2cos^(-1)(frac[sqrtx-1][sqrtx+1]...

If ` y=x^2cos^(-1)(frac[sqrtx-1][sqrtx+1])+x^2cosec^(-1)(frac[sqrtx+1][sqrtx-1])` then prove that `frac[d^2y][dx^2]=pi`

Promotional Banner

Topper's Solved these Questions

  • MATRICES DETERMINANTS PROBABILITY

    USHA PUBLICATION|Exercise EXERCISE|59 Videos

  • PRACTICE PAPER

    USHA PUBLICATION|Exercise PRACTICE PAPER|95 Videos

Similar Questions

Explore conceptually related problems

Differentiate if y=cos^(-1)frac (sqrt x-1)(sqrt x+ 1)+cosec^(-1)frac (sqrt x+1)(sqrt x- 1)

If y=tan^(-1)(frac[1+sinx][1-sinx])^(frac[1][2]) and z=log(frac[1+cosx][1-cosx]) , then prove that frac[dy][dx]=frac[-sinx][4]

If y=x^(-1)sincosec^(-1)frac[1][x] , then what is frac[dy][dx] ?

Solve (x+y+1)frac[dy][dx]=1

If y=sec^(-1)(sqrtx+1)/sqrtx+sin^(-1)fracsqrtx(sqrtx+1)then dy/dx= ____

Differentiate sqrtx(sqrtx+1)

cos^(-1)x+cos^(-1)y+cos^(-1)z=pi ,then prove that, x^2+y^2+z^2+xyz=1

Differentiate (sqrtx-1)/(sqrtx+1)

If sin^(-1)frac[x][5]+cosec^(-1)frac[5][4]=frac[pi][2] , then what is the value of x?

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. If ysqrt(x^2 +1) = log{sqrt(x^2 +1)- x} then prove that (x^2 +1) dy/dx...

    Text Solution

    |

  2. Find the equation of normal to the curve x^3 =4y which passes through ...

    Text Solution

    |

  3. If y=x^2cos^(-1)(frac[sqrtx-1][sqrtx+1])+x^2cosec^(-1)(frac[sqrtx+1][...

    Text Solution

    |

  4. Integrate int(frac[x-1][2x+1])dx

    Text Solution

    |

  5. int0^2[x^2]dx

    Text Solution

    |

  6. int0^(pi/2)e^x cosxdx

    Text Solution

    |

  7. Solve(x log x )dy/dx+y=2 log x.

    Text Solution

    |

  8. Find the area of the portion of the parabola y^2=4x bounded by the dou...

    Text Solution

    |

  9. If the sum of two unit vectors is a unit vector, show that the magnitu...

    Text Solution

    |

  10. Prove that : |veca + vecb|le|veca|+|vecb|.

    Text Solution

    |

  11. If A (1,0,-1), B (-2,4,-2) and C(1,5,10) be the vertices of a triangle...

    Text Solution

    |

  12. Find a symmetric form of the equation to the lines x +2y-z-2= 0 and 2x...

    Text Solution

    |

  13. Find the points of intersection of the line (x-1)/1=(y+2)/ 3 =(z-1)/(...

    Text Solution

    |

  14. Find frac[dy][dx] if y=tan^(-1)(frac[sqrt(a^2+x^2)+sqrt(a^2-x^2)][sqr...

    Text Solution

    |

  15. A curve passes through the point (2, 0) and slope of tthe tangent at a...

    Text Solution

    |

  16. Prove that int0^(pi)frac[xdx][1+sinx]=pi

    Text Solution

    |

  17. Find the solution of the following differential equations: (2x+3y-5)dy...

    Text Solution

    |

  18. Prove that cos^(-1)(frac[b+acosx][a+bcosx])=2tan^(-1)(sqrt(frac[a-b][a...

    Text Solution

    |

  19. Maximize:Z=10x1+12x2+8x3 "Subject to": x1+2x2 le 30 5x1 -7x3 ge 12 x1+...

    Text Solution

    |

  20. Let f: X rarr Y If there exists a map g:Y rarr X such that gof = id...

    Text Solution

    |