Home
Class 12
MATHS
If x=asin2t(1+cos2t) and y=bcos2t(1-cos2...

If `x=asin2t(1+cos2t)` and `y=bcos2t(1-cos2t),` show that at `pi/4,(dy)/(dx)=b/adot`

Text Solution

AI Generated Solution

To solve the problem, we need to find \(\frac{dy}{dx}\) given the equations for \(x\) and \(y\) in terms of \(t\), and then evaluate it at \(t = \frac{\pi}{4}\). ### Step 1: Differentiate \(x\) with respect to \(t\) Given: \[ x = a \sin(2t)(1 + \cos(2t)) \] ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA ENGLISH|Exercise All Questions|107 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA ENGLISH|Exercise All Questions|90 Videos

Similar Questions

Explore conceptually related problems

If x=asin2t(1+cos2t) and y=bcos2t(1-cos2t) , show that at t=pi/4 , (dy)/(dx)=b/a .

If x = a sin2t(1+cos2t) and y =b cos 2t(1-cos2t) , then show that ((dy)/(dx))_(t=pi//4) = (b)/(a) .

If x=asin2t(1+cos2t) and y=bcos2t(1-cos2t), find the values of (dy)/(dx) at t=pi/4 and t=pi/3dot

If x=sin^3t/(sqrtcos2t), y=cos^3t/sqrt(cos2t) show that dy/dx =0 at t=pi/6

If x=a(cos2t+2tsin2t) and y=a(sin2t-2tcos2t) , then find (dy)/(dx) .

If x=cost(3-2\ cos^2t) and y=sint(3-2sin^2t) find the value of (dy)/(dx) at t=pi/4

If x=2cost-cos2t , y=2sint-sin2t ,then at t=(pi)/(4) , (dy)/(dx)=

If x=sqrt(a^(sin^(-1)t)), y=sqrt(a^(cos^(-1)t)) , Show that (dy)/(dx)=-y/x .

If x=sqrt(a^(sin^(-1)t)), y=sqrt(a^(cos^(-1)t)) , show that (dy)/(dx)=-y/x

If x=e^(cos2t) and y=e^(sin2t) , prove that (dy)/(dx)=-(ylogx)/(xlogy)

RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If a>0, x=(t+1/t)^a ,y=a^(t+1/t),"find " (dy)/(dx)

    Text Solution

    |

  2. If x=a((1+t^2)/(1-t^2))"and"y=(2t)/(1-t^2),"f i n d"(dy)/(dx)

    Text Solution

    |

  3. If x=asin2t(1+cos2t) and y=bcos2t(1-cos2t), show that at pi/4,(dy)/...

    Text Solution

    |

  4. If x=(1+logt)/(t^2),y=(3+2logt)/t ,"f i n d"(dy)/(dx)dot

    Text Solution

    |

  5. If x=3sint-sin3t ,y=3cos t-cos3t ,"find "(dy)/(dx)" at "t=pi/3dot

    Text Solution

    |

  6. If sinx=(2t)/(1+t^2),tany=(2t)/(1-t^2),"f i n d"(dy)/(dx)dot

    Text Solution

    |

  7. Differentiate tan^(-1)((cosx)/(1+sinx)) with respect to sec^(-1)...

    Text Solution

    |

  8. If cosy=xcos(a+y), with cosa!=+-1, prove that (dy)/(dx)=(cos^2(a+y)...

    Text Solution

    |

  9. If f(x)=(log)(x^2)(logx), then f^(prime)(x) at x=e is 0 (b) 1 (c) 1...

    Text Solution

    |

  10. The derivative of the function cot^(-1){(cos2"x")^(1/2)}a tx=pi/6 is (...

    Text Solution

    |

  11. If f(x),g(x)a n dh(x) are three polynomials of degree 2, then prove th...

    Text Solution

    |

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

    Text Solution

    |

  13. If 3sin(x y)+4cos(x y)=5 then dy/dx=

    Text Solution

    |

  14. If f(x)=((x^l)/(x^m))^(l+m)((x^m)/(x^n))^(m+n)((x^n)/(x^l))^(n+l), the...

    Text Solution

    |

  15. d/(dx){tan^(-1)((cosx)/(1+sinx))}e q u a l 1/2 (b) x (c) (1-x^2)/(1...

    Text Solution

    |

  16. If y=sqrt(sinx+y) then (dy)/(dx)= (a) (sinx)/(2y-1) (b) (sinx)/(1-2y)...

    Text Solution

    |

  17. If y=1/(1+x^(a-b)+x^(c-b))+1/(1+x^(b-c)+x^(a-c))+1/(1+x^(b-a)+x^(c-a)...

    Text Solution

    |

  18. If sin^(-1)((x^2-y^2)/(x^2+y^2))=logat h e n(dy)/(dx)i se q u a lto ...

    Text Solution

    |

  19. If (1+x)^n=c0+C1x+C2x^2++Cn x^n ,using derivative prove that C1+2...

    Text Solution

    |

  20. Differentiate the following function with respect to x, "tan"(x^0+...

    Text Solution

    |